1
If three positive real numbers a, b, c are in A.P. such that abc = 4, ...
Progression and Series
2
The maximum sum of the series 20+19 (1/3)+18(2/3)+ is ...
Progression and Series
3
The largest term common to the sequences 1, 11, 21, 31, ... to 100 ter ...
Progression and Series
4
If the sum of m terms of an A.P. is the same as the sum of its n terms ...
Progression and Series
5
If the sides of a right angled triangle are in A.P. then the sines of ...
Progression and Series
6
If the ratio of the sum to n terms of two A.P.'s is (5n + 3); (3n + 4) ...
Progression and Series
7
150 workers were engaged to finish a piece of work in a certain number ...
Progression and Series
8
In an A.P. of which a is the first term, if the sum of the first p ter ...
Progression and Series
9
If S denotes the sum of first 'n' terms of an A.P. and (S3n - Sn-1)/s2 ...
Progression and Series
10
If a, b, and c are in A.P. then a² + c² - 8b^3 is equal to ...
Progression and Series
11
The number of terms of an A.P. is even; the sum of the odd terms is 24 ...
Progression and Series
12
If a, 1/b, c and 1/p, q,1/ r form two arithmetic progressions of the s ...
Progression and Series
13
Suppose that F(n + 1) = (2F(n) + 1)/2 for n = 1, 2, 3, ... and F(1) = ...
Progression and Series
14
If the sum of n terms of an A.P. is c * n(n - 1), where c ≠ 0, then th ...
Progression and Series
15
Consider an A.P. a1, a2, a3, ... such that a3 + a5 + a8 = 11 and a2 + ...
Progression and Series
16
16. If a, b, c,... are in A.P., then a, b, c, d,... are in A.P. if p, ...
Progression and Series
17
If a1, a2, a3,... are in A.P., then ap, aq,ar , ... are in A.P. if p, ...
Progression and Series
18
Let a₁, a₂, a₃ be terms of an A.P. If( a₁ + a₂ +... + ap )/( a₁ + a₂ ...
Progression and Series
19
If Sn denotes the sum of the first n terms of an A.P. whose first ter ...
Progression and Series
20
. Three numbers form an increasing G.P. If the middle number is double ...
Progression and Series
21
If a1, a2, a3 (a1 > 0) are three successive terms of a G.P. with comm ...
Progression and Series
22
. If |a| < 1 and |b| < 1, then the sum of the series 1 + (1 + a)b + (1 ...
Progression and Series
23
If (p + q)th term of a G.P. is 'a' and its (pq)th term is 'b' where a ...
Progression and Series
24
If the sides of a triangle are in G.P., and its largest angle is twic ...
Progression and Series
25
The value of log₂4 is ...
Progression and Series
26
If (1 + x⁴)(1+x)(1+x^2)....(1+x^128) = summation from r=0to n of xto ...
Progression and Series
27
If x, y, z are in G.P. and a^x = b^y = c^z, then ...
Progression and Series
28
The geometric mean between -9 and -16 is ...
Progression and Series
29
If S denotes the sum to infinity and Sn denotes the sum of n terms of ...
Progression and Series
30
The first term of an infinite geometric series is 21. The second term ...
Progression and Series
31
The number of terms common between the series 1+2+4+8 to 100 terms and ...
Progression and Series
32
After striking the floor, a certain ball rebounds (4/5) of the height ...
Progression and Series
33
The sum of an infinite G.P. is 57 and the sum of their cubes is 9747, ...
Progression and Series
34
If a² + b², ab + bc, and b² + c² are in G.P., then a, b, c are in ...
Progression and Series
35
Consider the ten numbers a, ar, ar², ..., ar⁹. If their sum is 18 and ...
Progression and Series
36
Let a = 111... 1 (55 digits), b = 1+10+10^2 + ... 10^4 , c = 1+10^5 +1 ...
Progression and Series
37
Let an be the nth term of a G.P. of positive numbers. If 100, 100, and ...
Progression and Series
38
The sum of 20 terms of a series of which every even term is 2 times th ...
Progression and Series
39
In a G.P., the first, third, and fifth terms may be considered as the ...
Progression and Series
