# 1.6 The nth term of a geometric progression

1.6 The nth Term of Geometric Progressions

(C) The nth Term of Geometric Progressions
a = first term
r = common ratio
n = the number of term
Tn = the nth term

Example 1:
Find the given term for each of the following geometric progressions.
(a) 8 ,4 ,2 ,...... T8
(b) ,  T6

Solution:

(a)

(b)

(D) The Number of Term of a Geometric Progression

Smart TIPS: You can find the number of term in an arithmetic progression if you know the last term

Example 2:
Find the number of terms for each of the following geometric progressions.
(a) 2, 4, 8, ….., 8192
(b)
(c)

Solution:
(a)

(b)

(c)

(E) Three consecutive terms of a geometric progression
If e, f and g are 3 consecutive terms of GP, then

Example 3:
If p + 20,   p − 4,    p −20 are three consecutive terms of a geometric progression, find the value of p.

Solution:
$\begin{array}{l}\frac{p-20}{p-4}=\frac{p-4}{p+20}\\ \left(p+20\right)\left(p-20\right)=\left(p-4\right)\left(p-4\right)\\ {p}^{2}-400={p}^{2}-8p+16\\ 8p=416\\ p=52\end{array}$