## Sum to finite terms - Advance

Dear Readers,

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-one number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3.

Q1.  If A=1+rz+r2z+r3z+.... then the value of r will be

•   (A+1/A)1/z
•  (A-1/A)1/z
•  (A+1/A)z
•   (A-1/A)z

(A-1/A)1/z

Q2. The sum to infinity of the following series 2+(1/2)+(1/3)+(1/22)+(1/32+(1/23))+(1/33)+.... will be

•  1/2
•  2/7
•  7/2
•  4

7/2

Q3. The sum of an infinite geometric series is 3. A series, which is formed by squares of its terms have the sum also 3. First series will be

•   3/2, 3/4, 3/8, 3/16, .....
•  1/2, 1/4, 1/8, 1/16, .....
•  2,4,8,16,....
•   None of the above

3/2, 3/4, 3/8, 3/16, .....

Q4.  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

•   a=3/7, r=7/3
•   a=4, r = 1/4
•   a=1/3,r=4
•  a=3,r=1/4

a=3,r=1/4

Q5.  Let n(>1) be a positive integer, then the largest integer m such that (nm+1) divides (1+n+n2+n3+........+n127) is

•  32
•  63
•  64
•  127

64

Q6.  If S denotes the sum to infinity and Sn the sum of n terms of the series 1+ 1/2 + 1/4 + 1/8+ .... such that S- Sn < (1/1000) then the least value of n is

•  8
•   9
•  10
•  11

10

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