SUM OF A GP 2

The sum of the 1st five terms of a geometrical progression is 484. If the common ratio is 3 find the 2nd term.

solution

S₅ = 484, G₁ = ?, r=3, n=5, A₂=?

 We use the summation formula to find the 1^st term.

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

Now we solve for the 2^nd term.

G_n = G₁r^n-1

G₂ = G₁r^2-1

G₂ = G₁r

G₂ = 4 x 3

     = 12

Hence the 2nd term is 12.

TRY THIS.........................

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