Sn=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. Sn=1275, r=2 (given). an=a×2n-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.