Arithmetic and geometric sequences
The question
−8, −1, 6, 13, … — the 25th term
d = 7
aₙ = −8 + (n − 1) × 7
a₂₅=−8 + 24 × 7
−8 + 168=160
a₂₅ = 160
- This is an arithmetic sequence: it changes by 7 each step (−1 − −8 = 7).
- The first term is already there, so to reach the 25th term you take the step only 24 times — that is (n − 1), not n.
- 24 steps of 7 is 168, and −8 + 168 = 160.
- So the 25th term is 160.
How it works.
- 01
This is an arithmetic sequence: it changes by 7 each step (−1 − −8 = 7).
- 02
The first term is already there, so to reach the 25th term you take the step only 24 times — that is (n − 1), not n.
- 03
24 steps of 7 is 168, and −8 + 168 = 160.
- 04
So the 25th term is 160.