Question

The first four terms of a sequence are \text{3, -6, 12, -24}. Write an explicit formula for this sequence, where n is any term number and a\left(n\right) is the nth term

Answer 1

Answer:

see explanation

Step-by-step explanation:

The terms form a geometric sequence with n th term

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

where a is the first term and r the common ratio

r = $\frac{a_{2} }{a_{1} }$ = $\frac{a_{3} }{a_{2} }$ = ......

r = $\frac{-6}{3}$ = $\frac{12}{-6}$ = - 2 and a = 3, hence

$a_{n}$ = 3 $(-2)^{n-1}$ ← explicit formula