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Question
Given a G.P. with a = 729 and 7th term 64, determine S7.
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Solution
गुणोत्तर श्रेणी का पहला पद, a = 729
मान लीजिए सार्व अनुपात = r
∴ 7वाँ पद = ar7-1 = ar6
729 r6 = 64
⇒ r6 = `64/729 = (2/3)^6`
∴ r = `2/3`
अब S7 = `("a"(1 - "r"^"n"))/(1 - "r")`
= `(729[1 - (2/3)^7])/(1 - 2/3)`
= `729 xx 3 xx [(2187 - 128)/2187]`
= `(729 xx 3)/2187 (2059)`
= 2059
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