GEOMETRIC PROGRESSION 3

The sum of the 1st eight terms of a geometrical progression is 19680. If the common ratio is 2 find the 1st term.

solution

S₈ = 19680,  G₁ = ?, r=3, n=8

S_n = G₁(rⁿ-1)/r-1

               

S₈ = G₁(r⁸-1)/ r-1

              

19680= G₁(3⁸-1)/3-1

               

19680= G₁(6561-1)

                    2

2 x 19680= G₁(6561-1) x 2¹

                         2₁

⁶39360 = 6560G₁

 6560      6560      

        

G₁= 6

Hence the 1st term is 6.

TRY THIS………….

The sum of the 1st nine terms of a geometrical progression is 4088. If the common ratio is 2 find the 1st term.