SEQUENCE AND SERIES A5

The sum of the 1st six terms of a geometrical progression is 728. If the common ratio is 3 find the 1st term.

solution

S₆ = 484 G₁ = ?, r=3, n=5

S_n = G₁(rⁿ-1)/r-1

               

S₆ = G₁(r⁶-1)/r-1

               

728= G₁(3⁶-1)/3-1

               

728= G₁(729-1)

                  2

2 x 728= G₁(728)

                  

1456= 728G₁

² 1456   =  G₁

  728

G₁ = 2

Hence the 1st term is 2.