# Arithmetic sequences #### Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered. #### Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals. #### Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now! ##### Examples
###### Lessons
1. Arithmetic sequence formula
Consider the arithmetic sequence: 5, 9, 13, 17, … .
1. Identify the common difference.
2. Determine the seventh term of the sequence.
3. Which term in the sequence has a value of 85?
2. Determine $t_1,d,t_n$ for the sequences in which two terms are given
1. $t_4=14$, $t_{10}=32$
2. $t_3=-14$, $t_{12}=-59$
3. Three consecutive terms of an arithmetic sequence are written in the form:
$1+2x,7x,3+4x$
Solve for the value of x.
###### Topic Notes
An arithmetic sequence (arithmetic progression) is a number sequence with a common difference between successive terms. By using the arithmetic sequence formula, we can easily find the value of a term and the common difference in the sequence.
• arithmetic sequence: a sequence with a common difference between successive terms
• The nth term, ${t_n}$ ,of an arithmetic sequence:
${t_n} = {t_1} + \left( {n - 1} \right)d$
where, ${t_n}$: nth term
${t_1}$: first term
$d$ : common difference