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

You can see that each term is twice the previous one, with inverted sign.

You double a number by multiplying it by two, and you change its sign by multiplying it by -1.

So, you multiply each term by 2 and by -1, which results in a multiplication by -2.

Since we start with 3, the terms are

$a_1 = 3$

$a_2 = 3\cdot (-2) = -6$

$a_3 = -6\cdot (-2) = 12$

and so on. So, the general term is

$a_n = 3\cdot(-2)^{n-1}$