# Arithmetic sequences

### Arithmetic sequences

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.

#### Lessons

• 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
• 1.
Arithmetic sequence formula
Consider the arithmetic sequence: 5, 9, 13, 17, … .
a)
Identify the common difference.

b)
Determine the seventh term of the sequence.

c)
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
a)
$t_4=14$, $t_{10}=32$

b)
$t_3=-14$, $t_{12}=-59$

• 3.
Three consecutive terms of an arithmetic sequence are written in the form:
$1+2x,7x,3+4x$
Solve for the value of x.