Question 14

The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to *n* terms of the G.P.

Answer

Let the G.P. be *a*, *ar*, *ar*^{2}, *ar*^{3}, …

According to the given condition,

*a *+ *ar* + *ar*^{2} = 16 and *ar*^{3} + *ar*^{4} + *ar*^{5} = 128

⇒ *a* (1 + *r* + *r*2) = 16 … (1)

*ar*^{3}(1 + *r* + *r*2) = 128 … (2)

Dividing equation (2) by (1), we obtain

Substituting *r* = 2 in (1), we obtain

*a* (1 + 2 + 4) = 16

⇒ *a* (7) = 16

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pranav kumar
2017-09-10 10:40:34

In a geometric progression,the sum of first 3 terms is 7 and the sum of next 3 terms is 56.Find the geometric progression.

Jeevan
2017-09-06 19:30:21

This problem help me thank you so much

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