JEE Questions for Maths Sequences And Series Quiz 14

The sum of the series 6 + 66 + 666 + ... upto n terms is

0%
0%
2)
0%
0%
None of these

If every term of a G.P with positive terms is the sum of its two previous terms, then common ratio of the series is

0%
1
0%
2)
0%
0%

0%
0%
2)
0%
0%
None of these

0%
3
0%
5
0%
7
0%
None of these

The product of n positive numbers is unity.Their sum is

0%
A positive integer
0%
Equal to n + 1/n
0%
Divisible by n
0%
Never less than n

Geometric mean of 7,7², 7³, ..........,7^{n is}

0%
0%
2)
0%
0%
None of these

If n geometric means be inserted between a and b then the n^th geometric mean will be

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

The G.M of the numbers 3,3², 3³, ... ,3ⁿ is

0%
0%
2)
0%
0%

If a,b,c are in G.P ., then

0%
a2, b2, c2 are in G.P
0%
a2(b + c), c2(a + b), b2(a + c) are in G.P
0%
0%
None of the above

0%
9
0%
9/2
0%
27/4
0%
15/2

If s is the sum of an infinite G.P, the first term a then the common ratio r given by

0%
0%
2)
0%
0%

If the product of three consecutive terms of G.P. is 216. and the sum of product of pair-wise is 156, then the numbers will be

0%
1, 3, 9
0%
2, 6, 18
0%
3, 9, 27
0%
2, 4, 8

0%
0%
2)
0%
0%

0%
15/23
0%
7/15
0%
7/8
0%
15/7

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

0%
xyz = x + y + z
0%
xz + yz = xy + z
0%
xy + yz = xz + y
0%
xy + xz = yz + x

The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

0%
– 12
0%
12
0%
4
0%
– 4

If S is the sum to infinite of a G.P., whose first term is a, then the sum of the first n terms is

0%
0%
2)
0%
0%
None of these

If x is added to each of number 3,9,21 so that the resulting numbers may be in G.P., then the value of x will be

0%
3
0%
1/2
0%
2
0%
1/3

Consider an infinite G.P with first term a and common ratio r, its sum is 4 and the second term is 3/4, then

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%
None of the above

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

In a G.P., t₂ + t₅ = 216 and t₄ : t₆ = 1: 4 and all terms are integers, then its first term is

0%
16
0%
14
0%
12
0%
None of these

If the arithmetic, geometric and harmonic means between two distinct positive real numbers be A, G and H respectively, then the relation between them is

0%
A > G > H
0%
A > G < H
0%
H > G > A
0%
G > A > H

If p^th, q^th, r^th and s^th terms of an A.P be in G.P., then (p - q), (q - r), (r - s) will be in

0%
G.P
0%
A.P
0%
H.P
0%
None of these

If the arithmetic and geometric means of a and b be A and G respectively, then the value of A - G will be

0%
0%
2)
0%
0%

0%
G.P
0%
A.P
0%
H.P
0%
None of these

0%
0%
2)
0%
0%

If the arithmetic mean of two numbers be A and geometric mean be G, then the numbers will be

0%
0%
2)
0%
0%

0%
A.P
0%
G.P
0%
H.P
0%
In G.P and H.P both

If a and b two different positive real numbers, then which of the following relation is true

0%
0%
2)
0%
0%
None of these

Three numbers whose sum is 15 are in A.P. If they are added by 1, 4 and 19 respectively they are in G.P.The numbers are

0%
2, 5, 8
0%
26, 5, –16
0%
2, 5, 8 and 26, 5, –16
0%
None of these

0%
0
0%
1
0%
2
0%
1/2

0%
A.P
0%
G.P
0%
H.P
0%
None of these

0%
0%
2)
0%
0%

If the (m + 1)^th, (n + 1)^th and (r + 1)^th terms of an A.P. are in G.P and m,n,r are in H.P., then the value of the ratio of the common difference to the first term of the A.P is