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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)

semsee45

Answer:

[tex]a_n=7\left(-3\right)^{n-1}[/tex]

Step-by-step explanation:

[tex]\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}}[/tex]

Given geometric sequence:

  • 7, -21, 63, ...

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

[tex]\implies r=\dfrac{a_3}{a_2}=\dfrac{63}{-21}=-3[/tex]

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

[tex]a_n=7\left(-3\right)^{n-1}[/tex]

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