Question

NO LINKS!! Find a formula for the nth term of the geometric sequence:

7, -21, 63, . . .

a_n =

Answer 1

To find the formula for the nth term of a geometric sequence, we can use the formula:

a_n = a_1 * r^(n-1)

where a_1 is the first term of the sequence, r is the common ratio, and n is the position of the term.

In this case, the first term of the sequence is a_1 = 7 and the common ratio is r = (-21)/7 = -3. Plugging these values into the formula, we get:

a_n = 7 * (-3)^(n-1)

Therefore, the formula for the nth term of the geometric sequence is:

a_n = 7 * (-3)^(n-1)

Answer 2

`a_n=7\left(-3\right)^(n-1)`

Explanation:

`\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^(n-1)$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}`

Given geometric sequence:

• 7, -21, 63, ...

To find the common ratio, divide a term by the previous term:

`\implies r=(a_3)/(a_2)=(63)/(-21)=-3`

Substitute the found common ratio and given first term into the formula to create an equation for the nth term:

`a_n=7\left(-3\right)^(n-1)`