Question

a G.P has 6 terms .if the 3rd term and the 4th terms are 28 and -56 respectively.find the common ratio,the first term ,and the sum of the G.P​

Answer 1

Hello,

Explanation:

`u_2=u_1*r\\u_3=u_1*r^2\\u_4=u_1*r^3\\\\(u_4)/(u_3) =r=(-56)/(28) =\boxed{-2}\\\\u_1=(u_3)/(r^2) =(28)/((-2)^2) =(28)/(4)=\boxed {7}\\\\\\\displaystyle\ s=\sum_(i=1)^6\ u_i\\\\=u_1*\sum_(i=1)^6\ r^(i-1)\\\\=7*((-2)^6-1)/(-2-1) \\\\=-7*(65)/(3) \\\\\\\boxed{s=-(455)/(3) }\\`