Question

The formula for any geometric sequence is an = a1 · rn - 1, where an represents the value of the nth term, a1 represents the value of the first term, r represents the common ratio, and n represents the term number. What is the formula for the sequence 2, -6, 18, -54, ...? an = 2 · 3n - 1 an = 2 · (-3)n - 1 an = 3 · 2n - 1 an = -3 · 2n - 1

Answer 1

The second choice

Explanation:

So first we would plug in the first term which is 2 so we would get
`an=2` times
`rn-1` so next we would see that the common ration is -3 since every time the number is being multiplied by -3. so then our equation would be
`an= 2` times
`-3n-1`. Now we would just find the choice that matches and it would be the second choice.

Answer 2

option 2

Explanation:

First term
`a_(1) = 2\\`

common ratio = r = second term ÷ first term

= -6 ÷2 = -4

Plug in the values of
`a_(1)` & r in the formula

`a_(n) = a_(1)*r^(n-1)\\\\\\a_(n)=2 * (-3)^(n-1)`