which formula can be used to find the nth term in a geometric sequence where (a_1 = 3) and (r = 2)?\n(a_n=3…

which formula can be used to find the nth term in a geometric sequence where (a_1 = 3) and (r = 2)?\n(a_n=3 + 2(n - 1))\n(a_n=3(n - 1)+2)\n(a_n=3^{n - 1}cdot2)\n(a_n=3cdot2^{n - 1})

which formula can be used to find the nth term in a geometric sequence where (a_1 = 3) and (r = 2)?\n(a_n=3 + 2(n - 1))\n(a_n=3(n - 1)+2)\n(a_n=3^{n - 1}cdot2)\n(a_n=3cdot2^{n - 1})

Answer

Explanation:

Step1: Recall geometric - sequence formula

The formula for the $n$th term of a geometric sequence is $a_{n}=a_{1}\cdot r^{n - 1}$, where $a_{1}$ is the first - term and $r$ is the common ratio.

Step2: Substitute given values

Given that $a_{1}=3$ and $r = 2$, substituting these values into the formula, we get $a_{n}=3\cdot2^{n - 1}$.

Answer:

$a_{n}=3\cdot2^{n - 1}$ (the fourth option)