### IB Mathematics HL – Arithmetic Sequences and Series

- Find the sum of the first 44 terms of the arithmetic sequence defined by the following formula

\(a_{n}=8+4n\) for \(n \geq 0\).

*Solution*

This is an arithmetic sequence with common difference \(d\) which can be found as following

\(d=a_{n+1}-a_{n}=8+4(n+1)-(8+4n)=4\)The first term is \(a=8\), the common difference is \(d = 4\), and \(n =44\).

In order to find the sum of the first \(n\) terms, we are using the following formula for an arithmetic series:

\(S_{n}=\frac{n}{2}[2a+(n-1)d]\), where in our case \(a=8, d=4, n=44\)

Therefore,

\(S_{44}=\frac{44}{2}[2(8)+(44-1)4]=\frac{44}{2}[16+172]=\) \(22(188)=4136\)