# How do you find the seventeenth term in the arithmetic sequence for which a=4.5 and d=0.2?

Feb 1, 2016

seventeenth term$= 7.7$

#### Explanation:

Recall the general term in an arithmetic sequence is written as:

${t}_{n} = a + \left(n - 1\right) d$

where:
${t}_{n} =$term number
$a =$first term
$n =$number of terms
$d =$common difference

To solve for the seventeenth term, substitute your known values into the equation:

${t}_{n} = a + \left(n - 1\right) d$

${t}_{17} = 4.5 + \left(17 - 1\right) \left(0.2\right)$

${t}_{17} = 4.5 + \left(16\right) \left(0.2\right)$

${t}_{17} = 4.5 + 3.2$

$\textcolor{g r e e n}{{t}_{17} = 7.7}$

Note that the seventeenth term is also ${t}_{17} = a + 16 d$. If you used this equation, it would produce the same answer:

${t}_{17} = a + 16 d$

${t}_{17} = 4.5 + 16 \left(0.2\right)$

${t}_{17} = 4.5 + 3.2$

$\textcolor{g r e e n}{{t}_{17} = 7.7}$

$\therefore$, the seventeenth term is $7.7$.