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

Asked by Pragya Singh | 1 year ago |  72

##### Solution :-

a = 729 and a7 = 64

Let r be the common ratio of the G.P.

Then we know that, an = a rn–1

a7 = ar7–1 = (729)r6

⇒ 64 = 729 r6

r6 = $$\dfrac{64}{729}$$

r6 = ($$\dfrac{2}{3}$$)6

r = $$\dfrac{2}{3}$$

And, we know that

$$s_n=\dfrac{a(1-r^n)}{1-r}$$

$$s_7=\dfrac{729[1-(\dfrac{2}{3})^7]}{1-\dfrac{2}{3}}$$

$$3\times 729=[1-(\dfrac{2}{3})^7]$$

$$(3)^7=\dfrac{(3)^7-(2)^7}{(3)^7}$$

= (3)7 - (2)7

= 2187 - 128

= 2059

Answered by Abhisek | 1 year ago

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