1
If three positive real numbers a, b, c are in A.P. such that abc = 4, then the minimum value of b is ...
2
The maximum sum of the series 20+19 (1/3)+18(2/3)+ is ...
3
The largest term common to the sequences 1, 11, 21, 31, ... to 100 terms and 31, 36, 41, 46, ... to ...
4
If the sum of m terms of an A.P. is the same as the sum of its n terms, then the sum of its (m + n) ...
5
If the sides of a right angled triangle are in A.P. then the sines of the acute angles are ...
6
If the ratio of the sum to n terms of two A.P.'s is (5n + 3); (3n + 4), then the ratio of their 17th ...
7
150 workers were engaged to finish a piece of work in a certain number of days. Four workers stopped ...
8
In an A.P. of which a is the first term, if the sum of the first p terms is zero, then the sum of th ...
9
If S denotes the sum of first 'n' terms of an A.P. and (S3n - Sn-1)/s2n-s2n-1 = 131, then the value ...
10
If a, b, and c are in A.P. then a² + c² - 8b^3 is equal to ...
11
The number of terms of an A.P. is even; the sum of the odd terms is 24, and of the even terms is 30, ...
12
If a, 1/b, c and 1/p, q,1/ r form two arithmetic progressions of the same common difference, then a, ...
13
Suppose that F(n + 1) = (2F(n) + 1)/2 for n = 1, 2, 3, ... and F(1) = 2. Then, F(101) equals ...
14
If the sum of n terms of an A.P. is c * n(n - 1), where c ≠ 0, then the sum of the squares of these ...
15
Consider an A.P. a1, a2, a3, ... such that a3 + a5 + a8 = 11 and a2 + a4 = -2, then the value of a1 ...
16
16. If a, b, c,... are in A.P., then a, b, c, d,... are in A.P. if p, q, r are in ...
17
If a1, a2, a3,... are in A.P., then ap, aq,ar , ... are in A.P. if p, q, r are in ...
18
Let a₁, a₂, a₃ be terms of an A.P. If( a₁ + a₂ +... + ap )/( a₁ + a₂ + ... + aq) =p^2/ q², then a6 ...
19
If Sn denotes the sum of the first n terms of an A.P. whose first term is a and common difference i ...
20
. Three numbers form an increasing G.P. If the middle number is doubled, then the new numbers are in ...
21
If a1, a2, a3 (a1 > 0) are three successive terms of a G.P. with common ratio r, the value of r for ...
22
. If |a| < 1 and |b| < 1, then the sum of the series 1 + (1 + a)b + (1 + a + a^2)b^2 + (1 + a + a^2 ...
23
If (p + q)th term of a G.P. is 'a' and its (pq)th term is 'b' where a, b ∈ R, then its pth term is ...
24
If the sides of a triangle are in G.P., and its largest angle is twice the smallest, then the commo ...
25
The value of log₂4 is ...
26
If (1 + x⁴)(1+x)(1+x^2)....(1+x^128) = summation from r=0to n of xto power r, then n is equal to ...
27
If x, y, z are in G.P. and a^x = b^y = c^z, then ...
28
The geometric mean between -9 and -16 is ...
29
If S denotes the sum to infinity and Sn denotes the sum of n terms of the series 1, 1/2, 1/4, 1/8, . ...
30
The first term of an infinite geometric series is 21. The second term and the sum of the series are ...
31
The number of terms common between the series 1+2+4+8 to 100 terms and 1+4+7+10 to 100 terms is ...
32
After striking the floor, a certain ball rebounds (4/5) of the height from which it has fallen. Then ...
33
The sum of an infinite G.P. is 57 and the sum of their cubes is 9747, then the common ratio of the G ...
34
If a² + b², ab + bc, and b² + c² are in G.P., then a, b, c are in ...
35
Consider the ten numbers a, ar, ar², ..., ar⁹. If their sum is 18 and the sum of their reciprocals i ...
36
Let a = 111... 1 (55 digits), b = 1+10+10^2 + ... 10^4 , c = 1+10^5 +10^10 +10^15+...+10^50 Then ...
37
Let an be the nth term of a G.P. of positive numbers. If 100, 100, and 4th terms of these ten terms ...
38
The sum of 20 terms of a series of which every even term is 2 times the term before it, and every od ...
39
In a G.P., the first, third, and fifth terms may be considered as the first, fourth, and sixteenth t ...
