sn=1275 an=640 r=2;a1

Question

find the indicated term for each geometric series described

Answer 1

S_n=a(rⁿ-1)/(r-1) is the formula for the sum of the terms of the series where a is the first term, n the number of terms and r the common ratio. S_n=1275, r=2 (given). a_n=a×2^n-1=640=5×2⁷, so a could be 5 and n-1=7, n=8. S₈=5(2⁸-1)=5×255=1275. This confirms that n=8 and a₁=5.