Given an arithmetic sequence $\{a_n\}$, $S_n$ is the sum of the first $n$ terms. We know $S_{30} = 390$ and $a_1 = 5$. We need to find $a_{30}$.

1. Problem Description

Given an arithmetic sequence $\{a_n\}$, $S_n$ is the sum of the first $n$ terms. We know $S_{30} = 390$ and $a_1 = 5$. We need to find $a_{30}$.

2. Solution Steps

The sum of the first $n$ terms of an arithmetic sequence is given by the formula:

$S_n = \frac{n(a_1 + a_n)}{2}$

In this case, we have $S_{30} = 390$, $a_1 = 5$, and $n=30$. We want to find $a_{30}$.

Plugging the given values into the formula, we get:

$S_{30} = \frac{30(a_1 + a_{30})}{2}$

$390 = \frac{30(5 + a_{30})}{2}$

$390 = 15(5 + a_{30})$

Divide both sides by 15:

$\frac{390}{15} = 5 + a_{30}$

$26 = 5 + a_{30}$

Subtract 5 from both sides:

$a_{30} = 26 - 5$

$a_{30} = 21$

3. Final Answer

21