Question

The formula uppercase S = StartFraction n (a Subscript 1 Baseline plus a Subscript n Baseline) Over 2 EndFraction gives the partial sum of an arithmetic sequence. What is the formula solved for an?

Answer 1

an=2S-a1n/n

Explanation:

Answer 2

`a_n = 2S - a_1`

Explanation:

Given

`S = (a_1 + a_n)/(2)`

Required

Determine the formula for
`a_n`

What this question implies is to solve for
`a_n`

`S = (a_1 + a_n)/(2)`

Multiply both sides by 2

`2 * S = (a_1 + a_n)/(2) * 2`

`2 S = a_1 + a_n`

Subtract
`a_1` from both sides

`2S - a_1 = a_1 - a_1 + a_n`

`2S - a_1 = a_n`

`a_n = 2S - a_1`

Hence; the formula to solve
`a_n` is
`a_n = 2S - a_1`