Sequences and Series · Mathematics · COMEDK
MCQ (Single Correct Answer)
If $\boldsymbol{k}$ is the arithmetic mean of two given quantities and $\boldsymbol{p}, \boldsymbol{q}$ are the geometric means between the same two quantities, then $\boldsymbol{p}^{\mathbf{3}}+\boldsymbol{q}^{\mathbf{3}}$ is:
Every term of a geometric progression is positive, and every term is the sum of the two preceding terms. Then the common ratio of the geometric progression is:
The product of three numbers in geometric progression is 8 and the sum of the product of the numbers taken in pairs is 14 . Find the numbers.
Let ' $\boldsymbol{a}$ ' and ' $\mathbf{b}$ ' be two numbers where $\boldsymbol{a}<\boldsymbol{b}$. The geometric mean of these numbers exceeds the smaller number by 12 and the arithmetic mean is smaller than the larger number by 24 . Then the value of $|\boldsymbol{b}-\boldsymbol{a}|$ 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
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
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
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
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
$$ \text { If } 6^{\text {th }} \text { term of a geometric progression is }-\frac{1}{32} \text { and } 9^{\text {th }} \text { term is } \frac{1}{256} \text { then } r \text { is } $$
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
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
$$ (32) \times(32)^{\frac{1}{6}} \times(32)^{\frac{1}{36}} \times-----\infty \text { is equal to } $$
The sum of $$n$$ terms of the series, $$\frac{4}{3}+\frac{10}{9}+\frac{28}{27}+\ldots$$ is
The value of $$\frac{1}{2 !}+\frac{2}{3 !}+\ldots+\frac{99}{100 !}$$ is equal to
If the sum of 12th and 22nd terms of an AP is 100, then the sum of the first 33 terms of an $$\mathrm{AP}$$ 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 $$\frac{y^3+z^3}{x y z}=$$ -----------
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
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
Total number of elements in the power set of A containing 17 elements is
The sum of the series $$(1 + 2) + (1 + 2 + {2^2}) + (1 + 2 + {2^2} + {2^3}) + ....$$ upto $$n$$ terms is
If a, b, c are in A.P., $$b-a,c-b$$ and a are in G.P., then a : b : c is
$${1 \over {2\,.\,5}} + {1 \over {5\,.\,8}} + {1 \over {8\,.\,11}} + ............. + {1 \over {(3n - 1)(3n + 2)}} = $$