Question

What is a formula for the nth term of the given sequence? 36, 24, 16...

Answer 1

Answer:

The formula to find the nth term of the given sequence is 54 · $\frac{2}{3} ^{n}$

Step-by-step explanation:

The formula for nth term of an geometric progression is :

$a_{n} = \frac{a_{1}(r^{n})}{r}$

In this example, we have $a_{1}$ = 36 (the first term in the sequence) and

r = $\frac{2}{3}$ (the rate in which the sequence is changing).

Knowing what the values for r and $a_{1}$ are, now we can solve.

$a_{n} = \frac{a_{1}(r^{n})}{r}$ = $\frac{36 (\frac{2}{3} ^{n}) }{\frac{2}{3} }$ = 54 · $\frac{2}{3} ^{n}$

Therefore, the formula to find the nth term of the given sequence is

54 · $\frac{2}{3} ^{n}$