SEQUENCE AND SERIES A9

The sum of the 1st five terms of a geometrical progression is 484. If the common ratio is 3 find the 1st term.

solution

S₅ = 484 G₁ = ?, r=3, n=5

S_n = G₁(rⁿ-1)/r-1

               

S₅ = G₁(r⁵-1)/r-1

               

484= G₁(3⁵-1)/3-1

               

484= G₁(243-1)

                  2

2 x 484= G₁(242)

                  

968= 242 G₁

⁴ 968   =  G₁

  242

G₁ = 4

Hence the 1st term is 4.