Geometric sequence nth term, step by step
A geometric sequence multiplies by the same factor every step, so its nth term is the start times the ratio raised to a power.
The question
3, 6, 12, … — the 9th term
r = 2
aₙ = 3 × 2^(n − 1)
a₉=3 × 2^8
3 × 256=768
a₉ = 768
- This is a geometric sequence: each term is the one before times 2 (6 ÷ 3 = 2).
- The first term is already there, so to reach the 9th term you multiply by 2 only 8 times — that is (n − 1), not n.
- 2 to the power 8 is 256, and 3 × 256 = 768.
- So the 9th term is 768.
How it works.
- 01
This is a geometric sequence: each term is the one before times 2 (6 ÷ 3 = 2).
- 02
The first term is already there, so to reach the 9th term you multiply by 2 only 8 times — that is (n − 1), not n.
- 03
2 to the power 8 is 256, and 3 × 256 = 768.
- 04
So the 9th term is 768.