the formula $s = \\frac{n(a_1 + a_n)}{2}$ gives the partial sum of an arithmetic sequence. what is the…

the formula $s = \\frac{n(a_1 + a_n)}{2}$ gives the partial sum of an arithmetic sequence. what is the formula solved for $a_n$?\n$a_n=\frac{2s - a_1n}{n}$\n$a_n=\frac{2s + a_1n}{n}$\n$a_n = 2s + a_1n + n$\n$a_n = 2s - a_1n + n$

the formula $s = \\frac{n(a_1 + a_n)}{2}$ gives the partial sum of an arithmetic sequence. what is the formula solved for $a_n$?\n$a_n=\frac{2s - a_1n}{n}$\n$a_n=\frac{2s + a_1n}{n}$\n$a_n = 2s + a_1n + n$\n$a_n = 2s - a_1n + n$

Answer

Explanation:

Step1: Multiply both sides by 2

$2S = n(a_1 + a_n)$

Step2: Divide both sides by n

$\frac{2S}{n}=a_1 + a_n$

Step3: Subtract $a_1$ from both sides

$a_n=\frac{2S}{n}-a_1=\frac{2S - a_1n}{n}$

Answer:

$a_n=\frac{2S - a_1n}{n}$ (First option)