Sequences and Series 4 Question 8

8. Consider an infinite geometric series with first term a and common ratio r. If its sum is 4 and the second term is 3/4, then

(2000, 2M)

(a) a=4/7,r=3/7

(b) a=2,r=3/8

(c) a=3/2,r=1/2

(d) a=3,r=1/4

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Solution:

  1. Since, sum =4 and second term =34.

It is given first term a and common ratio r.

a1r=4, ar =34r=34aa134a=44a24a3=4(a1)(a3)=0a=1 or 3

When a=1,r=3/4

and when a=3,r=1/4



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