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