GEOMETRIC SEQUENCE

Question

The third term of a geometric sequence is 3 and the sum of the second and third term is 60 . Determine the first three terms and general term Tn

Answer 1

The sequence is a₁, a₁r, a₁r², a₁r³, ...

a₃ = a₁r² = 3

a₁r + 3 = 60, so a₁r = 57

a₁ = 57/r

So, (57/r)r² = 3. 57r = 3. r = 1/19 and a₁ = 57/(1/19) = 1083.

a_n = 1083(1/19)^n-1

First 3 terms: 1083, 57, 3