Algebra · SS 2
nth term of a geometric progression (GP)
Find any term of a sequence that is multiplied by the same number each time.
- Tn = arn − 1
What the letters mean
- a
- the first term
- r
- the common ratio (2nd term ÷ 1st term)
- n
- the position of the term
Worked example
Find the 5th term of 2, 6, 18, …
Step 1: Read off a and r
a = 2, r = 6 ÷ 2 = 3
Step 2: n = 5
T5 = 2 × 34 = 2 × 81 = 162
Final answer: 162
See it
Play with this picture from the Geometric Progression lesson.
Each bar = the bar before × 3
T4 = a × r3 = 2 × 33 = 2 × 27 = 54
Sum of the first 4 terms: S4 = 80
Term number n4
First term a2
Common ratio r3