Algebra · SS 2
nth term of an arithmetic progression (AP)
Find any term of a sequence that goes up (or down) by the same amount each time.
- Tn = a + (n − 1)d
What the letters mean
- Tn
- the nth term
- a
- the first term
- d
- the common difference (2nd term − 1st term)
- n
- the position of the term
Worked example
Find the 10th term of 3, 7, 11, 15, …
Step 1: Read off a and d
a = 3, d = 7 − 3 = 4
Step 2: Use the formula with n = 10
T10 = 3 + (10 − 1) × 4 = 3 + 36 = 39
Final answer: 39
See it
Play with this picture from the Arithmetic Progression lesson.
Tₙ = 3 + (n − 1)×4 = 4n − 1
First term a3
Difference d4