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

Answer:

The second choice

Step-by-step 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

Answer:

option 2

Step-by-step 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

$a_{n} = a_{1}*r^{n-1}\\\\\\a_{n}=2 * (-3)^{n-1}$