Question 11.11.2.7: Finding the Sum of an arithmetic Sequence Find the sum: 60 +......

This is the sum S_{n} of an arithmetic sequence \{a_{n}\}{\mathrm{,~}} whose first term is a_{{1}}=60 and whose common difference is d = 4. The nth term is a_{n}=120. Use formula (2) to find n.

\ a_{n}=a_{1}+\;(n\;-\;1)d             Formula (2)

120=60+(n-1)\cdot4          a_{n}=120,a_{1} = 60,d=4

60=4(n-1)             Simplify.

15=n-1              Simplify.

n\,=\,16             Solve for n.

Now use formula (4) to find the sum S_{16}.

S_{n} ={\frac{n}{2}}\left(a_{1}+\,a_{n}\right)      (4)

S_{n} \overset{↑}{=}{\frac{n}{2}}(a_{1}\,+\,a_{n})