Question

128 The sum of n terms of the series 5/2-1 + 2/5 - ......
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Answer 1

Answer:

Given that, sum of n terms of a GP is 255 and common ratio is 2

i.e.

r−1

a(r

n

−1)

=255(∵r>1) ...(i), where r is common ratio and a is first term

Also, n

th

term is 128

i.e. ar

n−1

=128 ...(ii)

and r=2 ....(iii)

From Equations (i), (ii) and (iii)

a(2)

n−1

=128 ....(iv)

and

2−1

a(2

n

−1)

=255 .....(v)

On dividing Eq (v) by Eq (iv), we get

2

n−1

2

n

−1

=

128

255

⇒2−2

−n+1

=

128

255

⇒2

−n

=2

−8

⇒n=8

On putting n=8 in Eq (iv), we get

a.2

7

=128=2

7

⇒a=1

Explanation:

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