the common ratio in a geometric series is 4 and the first term is 3. find the sum of the first 8 terms in…

Explanation:

Step1: Recall sum formula for geometric series

The sum formula for the first $n$ terms of a geometric series is $S_n=\frac{a(1 - r^n)}{1 - r}$ when $r\neq1$, where $a$ is the first - term, $r$ is the common ratio, and $n$ is the number of terms.

Step2: Identify values of $a$, $r$, and $n$

Given that $a = 3$, $r = 4$, and $n = 8$.

Step3: Substitute values into the formula

$S_8=\frac{3(1 - 4^8)}{1 - 4}$. First, calculate $4^8=65536$. Then $1-4^8=1 - 65536=-65535$. The denominator $1 - 4=-3$. So, $S_8=\frac{3\times(-65535)}{-3}$. The $3$ in the numerator and the $- 3$ in the denominator cancel out, and we get $S_8 = 65535$.

Answer:

$65535$