let a0 = r, a1= dr, a2=d^2r, a3=d^3r, ......, an=d^nr then we have (1) a0 + a1 = dr + r = r(1+d) =7 (2) a0+a1+a2 + ....+ a5 = 91 r+dr+d^2r+d^3r+d^4r+d^5r = 91 r(1+d) + d^2r(1+d) + d^4r(1+d) = 91 using (1), we have 7+7d^2 +7d^4 = 91 Solving this quadratic equation, we have d^2 = 3 (the other root d^2 = -4 does not make sense). We want a0 + a1 +a2 +a3 = r+dr+d^2r+d^3r = r(1+d) + d^2r(1+d) = 7+7d^2 = 7 + 7*3 = 28 Therefore the answer is 28. done. |