# IB μαθηματικά HL- Sequences and Series

### IB Mathematics HL – Arithmetic Sequences and Series

1. 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,

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