Question

What fomula can be used to describe the sequence? -2/3,-4,-24,-144

Answer 1

This is a geometric sequence with n th term formula

$a_{n}$ = $a_{1}$$(r)^{n-1}$

where r is the common ratio and $a_{1}$ the first term

here $a_{1}$ = - $\frac{2}{3}$ and

r = $\frac{-144}{-24}$ = $\frac{-24}{-4}$ = 6

$a_{n}$ = - $\frac{2}{3}$$(6)^{n-1}$

or in terms of x

f(x) = - $\frac{2}{3}$$(6)^{x-1}$