If we assume the common ratio of the second series is r^2, then we have : a + ar + a r^2 + a r^3 + ........ = 15 a^2 + (ar)^2 + (a r^2)^2 + (a r^3)^2 + ........ = 45 i.e. a(1+r+r^2 + r^3 + .....) =15 a^2(1+r^2+r^4 + r^6 + .....) =45 i.e. a/(1-r) = 15 a^2/(1-r^2) =45 Solving the two equations above, we obtain r= 2/3 and a =5 Hence, the first term of the first series is a = 5 note: Maybe it is a typo that the common ratio of the second series is r rather than r^2 ? |
