Question

The sum of the first nine terms in a sequence is 49,205. Each term is 3 times the previous term. What is the third term?

Answer 1

a₃ = 32 805

Explanation:

Each term is 3 times the previous term:

r = 3

The sum of the first nine terms in a sequence is 49,205:

`S_n=a_1\cdot(1-q^n)/(1-q)\\\\\\49205=a_1\cdot(1-3^9)/(1-3)\\\\49205=a_1\cdot(1-19683)/(-2)\\\\49205=a_1\cdot9841\\\\a_1=5`

What is the third term?

`a_n=a_1\cdot q^(n-1)\\\\a_3=5\cdot3^8=32805`