Given a G.P with a = 729 and 7^th term 64, determine S₇

Solution:

It is given that

a = 729 and a₇ = 64

Let r be the common ratio of the G.P.

It is known that Therefore, a = ar^{n - 1}

⇒ a = ar^{7 - 1} = ar⁶

⇒ 64 = 729r⁶

r⁶ = (2/3)⁶

r = 2/3

Also,

S_n = a (1 - rⁿ)/(1 - r)

= 729 (1 - (2/3)⁷)/(1 - 2/3)

= 3 x 729 (1 - (2/3)⁷)

(3)⁷ [(3)⁷ - (2)⁷]/(3)⁷

(3)⁷ - (2)⁷

= 2187 - 128

= 2059

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NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.3 Question 15

Given a G.P with a = 729 and 7^th term 64, determine S₇

Summary:

Given that the first term =729 and the 7th term is 64 we find out that the sum of seven numbers is 2059