Question

The formula S=n(a^1+a^n)/2 gives partial sum of an arithmetic sequence. What is the formula solved for a^n?

Answer 1

i am going to make a guess that this says
\[\large S=\frac{n(a_1+a_n)}{2}\] am i right?

Answer 2

yeah.

Answer 3

and you want to solve for \(a_n\)

Answer 4

yeah.

Answer 5

multiply both side by 2 first and get
\[2S=n(a_1+a_n)\]

Answer 6

divide both sides by \(n\) and get
\[\frac{2S}{n}=a_1+a_n\]

Answer 7

then subtract \(a_1\) from both sides and you are done
\[\large\frac{2S}{n}-a_1=a_n\]

Answer 8

thank you