## Arithmetic Series, IB Math HL

Discussions for the Core part of the syllabus. Algebra, Functions and equations, Circular functions and trigonometry, Vectors, Statistics and probability, Calculus. IB Maths HL Revision Notes

### Arithmetic Series, IB Math HL

IB Mathematics HL – Arithmetic Sequences and Series

How can we find the sum of the first 44 terms of the arithmetic sequence defined by the following formula?
$a_{n}=8+4n$ for $n \geq 0$

Thanks
Jack

Posts: 0
Joined: Mon Jan 28, 2013 8:08 pm

### Re: Arithmetic Series, IB Math HL

IB Math HL – Arithmetic Sequences and Series

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,

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

$=22(188)=4136$

Hope these help!!
miranda

Posts: 268
Joined: Mon Jan 28, 2013 8:03 pm

### Re: Arithmetic Series, IB Math HL

Thanks!
Jack

Posts: 0
Joined: Mon Jan 28, 2013 8:08 pm