Sequences And Series - Algebra - Mathematics Previous Year Questions

$${1 \over {2\,.\,5}} + {1 \over {5\,.\,8}} + {1 \over {8\,.\,11}} + ............. + {1 \over {(3n - 1)(3n + 2)}} =$$

If a, b, c are in A.P., \(b-a,c-b\) and a are in G.P., then a : b : c is

The sum of the series \((1 + 2) + (1 + 2 + {2^2}) + (1 + 2 + {2^2} + {2^3}) + ....\) upto \(n\) terms is

If \(S = {{{2^2} - 1} \over 2} + {{{3^2} - 2} \over 6} + {{{4^2} - 3} \over {12}}\, + \,...\) upto 10 terms, then S is equal to

Total number of elements in the power set of A containing 17 elements is

The first and fifth terms of an A.P. are \(-14\) and 2 respectively and the sum of its n terms is 40. The value of n is

If three numbers \(a, b, c\) constitute both an A.P and G.P, then

Le \(x\) be the arithmetic mean and \(y, z\) be the two geometric means between any two positive numbers, then \(\frac{y^3+z^3}{x y z}=\) -----------

The sum of four numbers in a geometric progression is 60 , and the arithmetic mean of the first and the last number is 18 . Then the numbers are

The sum of first three terms of a geometric progression is 16 and the sum of next three terms is 128 . The sum to \(\mathrm{n}\) terms of the geometric progression is

$$\text { If } 6^{\text {th }} \text { term of a geometric progression is }-\frac{1}{32} \text { and } 9^{\text {th }} \text { term is } \frac{1}{256} \text { then } r \text { is }$$

If two positive numbers are in the ratio \(3+2 \sqrt{2}: 3-2 \sqrt{2}\), then the ratio between their A.M (arithmetic mean) and G.M (geometric mean) is

Consider an infinite geometric series with first term '\(a\)' and common ratio '\(r\)'. If the sum of infinite geometric series is 4 and the second term is \(\frac{3}{4}\) then

A number consists of three digits in geometric progression. The sum of the right hand and left hand digits exceeds twice the middle digit by 1 and the sum of left hand and middle digits is two third of the sum of the middle and right hand digits. Then the sum of digits of number is

$$(32) \times(32)^{\frac{1}{6}} \times(32)^{\frac{1}{36}} \times-----\infty \text { is equal to }$$

Given \(a, b, c\) are three unequal numbers such that \(\mathrm{b}\) is arithmetic mean of \(a\) and \(c\) and \((b-a),(c-b), a\) are in geometric progression. Then \(a: b: c\) is

A geometric progression consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying odd places, then the common ratio of the G.P is

The sum of \(n\) terms of the series, \(\frac{4}{3}+\frac{10}{9}+\frac{28}{27}+\ldots\) is