The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms. - Mathematics

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Sum

The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.

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Solution

Let the sum of n terms of the G.P. be 315.

It is known that, Sn `(a(r^n - 1))/(r - 1)`

given geometric progression

5 + 10 + 20 + 40 + …….

Sum of n terms = `(5(2^"n" - 1))/(2 -1) = 315`

∴ 2n – 1 = 63

or 2n = 64 = 26

n = 6

6th term = 5 × 26 – 1

= 5 × 25

= 5 × 32

= 160

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Chapter 9: Sequences and Series - Miscellaneous Exercise [Page 199]

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NCERT Mathematics Class 11
Chapter 9 Sequences and Series
Miscellaneous Exercise | Q 8 | Page 199

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