Arithmetic sequence check my work

Question

Let $\{a_j\}$ be an arithmetic sequence with the following conditions:

Given $s_{16} = 376$ and $a_{16} = 46$, find $a_1$.

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

$376 = \dfrac{16}{2} \cdot (a_1 + 46)$
$47 - 46 = 1$
$a_1 = 1$

common ratio $= -5$?

Don't need that value however.

Answer 1

Your approach is correct, but it would be better to write it something like $$376=\frac {16}2(a_1+46)\\\frac {376}8=a_1+46\\1=a_1$$ Your statement that $47-46=1$ is correct, but is not motivated. This is why we keep the variables in the equations.

The difference (not common ratio) is $5$, not $-5$ as the terms are increasing.

Answer 2

After $376 = \dfrac{16}{2} \cdot (a_1 + 46)$ you get, $a_1+ 46=376\times \frac{2}{16}$ or, $a_1=47-46=1$ so finally you get $a_1=1$.