Question

एक गुणोत्तर श्रेणी का प्रथम पद a = 729 तथा 7वाँ पद 64 है तो S₇ ज्ञात कीजिए?

Answer 1

First term of the geometric progression, a = 729

Let common ratio = r

∴ 7th term = ar^7-1 = ar⁶

729 r⁶ = 64

⇒ r⁶ = `64/729 = (2/3)^6`

∴ r = `2/3`

Now 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