In a geometric progression, if the ratio of the sum of the first 5 terms to the sum of their reciprocals is 49, and the sum of the first and the third term is 35, then the first term of this geometric progression is:
Solutions · 1
Official solution
\[\frac{S_5}{S_5'}=\frac{a(r^5-1)/(r-1)}{a^{-1}(r^{-5}-1)/(r^{-1}-1)}=a^2r^4=49.\]
So ar2=7 ... (i) (taking the positive root).
Also a+ar2=35 ... (ii). Substituting (i): a+7=35⇒a=28.