1) Find the 12th term of the sequence 1, 2, 4, 8.....
A) 2048 B)1024 C)512 D)5126
2) The first and the 6th term of a GP are 2 and 64 respectively find the common ratio.
A) 3 B) 4 C) 5 D) 2
3) if the 5th and 10th terms of a GP 32 and 1024 respectively, find the first term and the common ratio.
A) 2,2 B) 2, 3 C) 1,2 D) 2,4
4) find the 4th term of the GP whose 5th term is 32 and 8th term is 256.
A) 14 B)16 C)18 D) 20
5) In a G. P., the common ratio is equal to the 1st term. if the fifth term is 243, find the 10th term.
A) 49049. B)59049 C)59059 D)69079
6) Insert three geometric means between 3 and 48.
A)6,18,24 B)6,24,36 C)6,12,24 d)N
7) find the the three numbers in GP whose sum is 14 and product is 64.
A) 2,68, B) 1,4,16 C) 2,4,8 D) none
8) the sum of three numbers in GP is 26 and their product is 216 find the numbers.
A) 2,6,8 B) 2,6,18 C) 2,16,18 D) n
9) The sum of the first 20 terms of a GP is 244 times the sum of its first 10 terms. find the common ratio
A) √3 B) -√3 C) both A& B D) N
10) Sum of the first three terms of of a GP is to the the sum of the first six terms as 125: 152 find the common ratio of the GP
A) 0.40. B) 0.50 C)0.75. D) 0.60
11) the sum of the three terms in GP is 14. if the first two terms are increased by 1and the third term is decreased by 1, the resulting number are in AP. the GP is:
A) 2,4,,8 B) 8,4,2
C) both A &B D) either A or B
12) The sum of the first three terms of a GP is 7 and the sum of their squares is 21.determine the 5th term of the GP term of the GP.
A) 8 B) 32 C) 16 D) 64
13) the third term of a GP is 4, the product of the first 5 term is
A) 4³. B) 4^ 5 C) 4⁴ D)
14) the Arithmetic mean of two numbers is 10 and their GM is 8. find the numbers.
A) 4,12. B) 2,18 C) 4,16 D) 10 10
15) The A.M of two numbers is 34 and their GM is 16. find the numbers
A) 4,64. B) 17, 17 D) 16,32 D) N
16) If the 3rd term of a GP is the square of the 1st term and if the 5th term is 64; find the series.
A) 4, 8,16,32 B) 4 - 8, 16 ,- 32
C) either A or B D) none
17) if you save Rs 1 today, Rs 2 the next day, Rs4 the succeeding day and so on, what will be the total savings in 12 days?
A) ₹1023 B)₹2047 C) ₹2047 D)N
18) A person decides save ₹2 in January, # 4 in February, ₹ 8 in March, ₹16 in April and so on up to the end of a year. how much amount will he save during the whole year?
A) ₹8190 B) ₹4095
C)₹2048 D)₹8192
19) Taking the data from the previous question, how much this person will save the month of October.
A) ₹2018 B)₹512
C)₹1024 D)₹ 2056
20) how many terms of the series series 1 + 3 + 9 +27... must be taken so that their sum is 364?
A) 5. B) 6. C) 8 D) 9
21) how many terms of the series series 2 + 4 + 8....must be takes so as to have their sum equal to 32766 ?
A) 12 B) 13 C) 15 D) 14
22) If 5, x, y, z, 405 are the five terms terms of a GP. find f GP find the values of x ,y , z.
A)15 ,45 ,125 B) 15 ,35 ,135
D)15,45,135. D) 25,45,135
23) the sum of first 6 terms of a GP is 9 times the sum of the first three terms.find the common ratio
A) 2 B) 3 C) 4. D) 8
24) the common ratio, last term, and the sum of GP are 3,486 and 728 respectively.
A) 4 B) 6 C) 8 D) 2
25) In a GP, the sum to first n terms is 4095, common ratio is 2 and the last term is 2048. find n.
A) 10 B) 11. C) 12 D)15
26) the second term of a GP is b, and the common ratio is r. if the product of the first three terms of this GP is 64. find b is 64
Aa) 12 B) 4 C) 6 DD) 18
27) divide 42 in three parts such that the parts form a GP and their product is 512 .
A) 2, 8, 16 B) 2, 8, 32
C) 4, 8 30 D) NONE
28) find the three real numbers in GP whose sum is 38 and product is 1728.
A) 8,14,16 B)4,12,22C)8,12,18 D)N
29) Find the least value of n for which the sum 1 + 3 + 3² +3³+ to n terms is greater than 7000
A) 8 B) 11 C)10 D) 9
30) the sum of three numbers in GP is 70, if the two extremes be multiplied each by 4 and the mean by 5, the product are in AP. find the numbers.
A) 10,20,40 B) 15,25,30
C) 5, 15 50. D) 10, 15,45
31) A sum of ₹312 is divided among four persons a, b, c,d. the amount received by them form a GP.. if a and d together receives ₹ 252, find the amount received by each person separately.
A) 2,5,55,250 B)12,5,55,240
C) 2,10,50,250. D) none
32) the sum of three numbers in AP is 15 if 1,4, 19 are added to them respectively, the resulting number are in GP. find the numbers.
A) 2,5,8 B) 3,6,9 C) 2,7,12 D)12,7,2
33) three numbers whose sum is 18 are in AP, if 2, 4 ,11 are added to them added respectively, the result are in GP. determine the numbers.
A) 3,6,9 B)18,6,-6 C) neither of a nor b D) either A or B
34) the sequence of three numbers a, b ,c are in AP whose sum is 18. if a and b are each increased by 4 and c is increased by 36.the new number form a GP. find a,b,c. find a b c
A) -2,6,14 B) 46,6 -34 C) both a and b D) either A or B
35) the product of three numbers in GP is 729 and the sum of their squares is 819. one of the numbers are
A) 3 B) 9 C) 27 D)all of the above
36) three numbers are in AP and their sum is 15. if 1,3,9 be added to them respectively. they form a GP. find the numbers.
A) 15,5,-5 B) 3,5,7 C) 7 ,- 5, 3
D) either A or B
37) fourth term of a GP is 27 and the 7th term is 729 find the GP.
A) 1,3,9 B)1,9,27 C)1,2,4 D)- 1,3 - 9
38) the seventh term of a GP term of a GP 8 times the fourth term and fifth term is 48. find the GP
A)3,9,27 B)3,6,12
C)-3,6,12 D) 2,6,18
39) if the GP's 5,10,20...and1280 640,320 have their nth terms equal, find the value of n
Aa) 2, B) 7 C) 5 D)8
40) find three numbers in GP whose sum is is 65 and whose product is 3375
A) 510,50 B) 5,15,45
C) 10,15,40 D) 40, 5,20
41) find three numbers in GP whose sum is 38 and their product is 1728.
A) 8,12,18 B) 8,16,64
C) 4,8,16. D) 4,,16,18
42) the sum of three numbers in GP 21 and the sum of their squares is 189 find the numbers find the numbers.
A)3,5,14 B)3,612
C) 2, 8,11 D) 2, 6,13
43) the sum of three numbers in GP is 14. If the first two terms are each increased by 1 and the third term decreased by 1, the resulting numbers are in AP. find the numbers.
A) 2,6,8. B) 1,4,8
C) 2,4,8 D) 8,4,1
44) the product of three numbers in GP is 216 in GP. if 2,8,6 be added to them, the results are in AP. find the numbers.
A) 2,6,18 B)1,7,18
C) 2,8,14 D)3,9 ,27
45) find three numbers in G. P. Whose products is 729 and the sum of their products in pairs is 819.
A) 3,9,27 B) 1,9,81
C) 3,27,81 D) 9,27,81
46) The sum of three numbers in G. P is 56, if 1,7,21 are substracted from the numbers respectively, resulting numbers form the cosecutive terms of an AP. find the numbers.
A) 8,34,32 B) 8,16,32
c) 6,20,36 D) 4,8,32
47) How many terms of the GP. 3, 3/2,3/4,.... be taken together to make 3069/512.
A)6. B) 10. C) 8. D) 12
48) How many terms of the series 2+6+18+... must be taken to make the sum equal to 728
A) 6. B) 10. C) 8. D)12
49) How many terms of the sequence√3, 3, 3√3,.... must be taken to make the sum 39+13√3
A) 6. B) 20. C) 8. D) 12
50) The sum of n terms of the G. P 3,6,12,.....is 381. Find the value of n.
A) 6 B) 10 C) 7 D) 13
51) The common ratio of a GP is 3 and the last term is 486. If the sum of these terms be 728. Find the first term.
A) 2. B) 4. C) 3. D) 5
52) The ratio of the sum of first three terms is to that first 6 terms of a GP is 125:152. Find the common ratio.
A) 0.50. B) 0.60. C) 0.75. D) 1.25
53) Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an AP and the ratio of 7th and (m-1)th numbers is 5:9. Find the value of m.
A) 41 B) 12 c) 14 D) none
54) Let x be the AM and y,, z be 2 GM between a y two positive numbers. Then find the value of (y³+z³)/xyz
A) 1 B) 2 C) 3 D) none
55) Find the sum of the following
A) 1 + 1/3+1/3²+.......
i) 1/2. ii) 1/3 iii)3/2. iv) none
B) 1/4+3/16+9/64+.......
i) 7 ii) 1/7 iii)7/11 iv) 5/7
C) 1+1/(1.05)+1/(1.05)²+......
i) 21 ii) 12. iii) 11 iv) 5
56) The sum of an infinite G. P whose first term is 28 and the fourth term is 4/49 is:
A) 28/3B) 92/3C) 91/3. D) 102/31
57) The first of an infinite GP series, whose sum to infinity is 8 and second term is 2 is:
A) 2. B) 4. C) 8. D) 5
58) The sum of the first 2 terms of a GP is 5/3 and the sum to infinity is 3. The first term of the GP is:
A) 1. B) 2/3. C) 3/2. D) 2
59) For the series given in the previous question, what is its common ratio:
A) 1. B) 2/3. C) 3/2. D) 2
60) For a GP series, sum to infinity is 15 and the sum of the squares of the terms of this same series, to infinity is 45. What is the common ratio of the series?
A) 1. B) 2/3. C) 3/2. D) 2
61) If in an infinite GP, each term is twice the sum of all succeeding terms, than what is the value of common ratio, if it's first term is 2
A) 1/2. B) 1/3. C) 1/4. D) 1/5
62) If x,y,z be in GP, then logx, logy, logz in
A) GP. B) HP. C) AP. D) none
63) The sum of the GP a+b...+l is
A) (bl-a²)/(b-a). B) (bl-a)/(b-a)
C) ((l -a²)/(b-a). D) (b-a)/(b-a)
64) If x,y,z be the pth, qth, and rth terms respectively, both of an AP and GP series, find the value of
xʸ⁻ᶻ yᶻ⁻ˣ zˣ⁻ʸ
A) 0. B) 1. C) -1. D) none
65) In a GP (p+q)th term is m and (p-q) is n. Find its pth term.
A) √m. B) √n C) √mn. D) √(m+n)
66) If a,b,c are in GP, then which of the following/s is/are true.
A) a(b²-c²)=c(a²-b²)
B) 1/(a+b), 1/2b, 1/(b+c) are in AP
C) a²b²c²(1/a³+1/b³+1/c³)
=a³+b³++c³. D) all of the above
67) If a,b,c,d are in GP, then (a+b),(b+c),(c+d) are in:
A) AP. B) GP. C) HP. D) both A, B not C
68) a,b,c,d are in GP then (a²+b²), (b²+c²),(c²+d²) are in:
A) GP B) AP. C) both A,B D) none
69) If a,b,c,d are in GP, then 1/(a+b), 1/(b+c), 1/(c+d) are in:
A) HP. B) AP. C) GP. D) All
70) If p,q,r, are in AP, q,r,s are in GP and r,s,t are in HP, then p,r,t are in
A) AP. B) GP. C) HP. D) none
71) If a,b,c are in GP and aˣ=bʸ= cᶻ
Then 1/x, 1/y , 1/z are in:
A) GP. B) AP. C) both A, B D) HP
72) If a,b,x,y,z are positive numbers such that a,x,b are in AP, a,y,b are in GP and (a+b)z= 2ab, then x,y,z are in:
A) AP. B) HP. C) GP. D) none
73) If x,y,z be respectively the pth, tth, and rth terms of a GP, then
xᵗ⁻ʳ yʳ⁻ᵖ zᵖ⁻ᵗ
a) 0 b) 1 c) -1 d) none
74) If p,t,r are in AP and x,y,z are in GP, then xᵗ⁻ʳ yʳ⁻ᵖ zᵖ⁻ᵗ
a) 0 b) 1 c) -1 d) none
75) What is the ratio of two positive numbers, when the ratio 1 of their A. M to G. M is 5:3
A) 1:9 B) 1:5 C) 3:5 D) 9:1
76) K is the AM of two given numbers and p,q are the two of GM between the same two quantities, then the value of p³+q³
A) 2pq. B) 2pqK. C) 2K. D) none
77) In a set of four numbers, the first three are in A GP, and the last three are in AP, with common difference of 6. If the first numbers is the same as the fourth: the numbers are:
A) 8,4,2,8 B) 8,-4,2,8
C) 4,2,1,4 D) 4, -2,1,4
78) If a,b,c are in GP and x,y be the AM between a,b,c. Then which of the following/s is/are true?
A) a/x +c/y= 2. B) 1/x +1/y= 2/b
C) both A,B. D) neither A nor B
79) The first, tenth and twenty-eight term of an AP are three successive terms of a GP. Find the common ratio of the GP. Given that the sum of the first 28 terms of the AP is 210. Find its first term..
A) 2,2. B) 2,3. C) 3,2. D) -3,2
80) Find the four Integers a,b,c,d such that a,b,c are in GP; b,c,d are in AP and c+d= 20 & a+b= 6.
A)4,8,12,4 B) 2, 4, 6, 8,
C) 2, 4,8,12. D) none
81) Find three unequal positive integers a,b,c such that 2,a,b form an AP and a,b,c form a GP.
A) 4,8,12. B) 4,6,7
C) 4,8,11. D) 4,6,9
