Question:
The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.
Answer:
Let number of terms in GP =n
Sum of n terms = a*(rn - 1)/(r-1) = 315
=>5*(2n -1)/(2-1) = 315 (a = 5, r = 2)
=>2n -1 = 315/5
=>2n -1 =63
=>2n = 63+1
=>2n = 64
=>2n = 26
=>n = 6
So number of terms in the series = 6
Last term in the Series = a*rn-1
= 5*26-1
= 5*25
= 5*32
= 160
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