# Arithmetic sequences

#### All You Need in One Place

Everything you need for better marks in primary, GCSE, and A-level classes.

#### Learn with Confidence

We’ve mastered the UK’s national curriculum so you can study with confidence.

#### Instant and Unlimited Help

0/6
##### 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.
###### Free to Join!
StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun - with achievements, customizable avatars, and awards to keep you motivated.
• #### Easily See Your Progress

We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.
• #### Make Use of Our Learning Aids

###### Practice Accuracy

See how well your practice sessions are going over time.

Stay on track with our daily recommendations.

• #### Earn Achievements as You Learn

Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.
• #### Create and Customize Your Avatar

Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.
###### 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