# How do you find 37th term of the sequence {4, 7, 10, ....}?

Aug 2, 2018

$112$ is the 37th term

#### Explanation:

This is an arithmetic sequence

So, ${T}_{n} = a + \left(n - 1\right) d$
where $a$ is your first term, $n$ is your nth term and $d$ is the difference between 2 adjacent terms

Looking at the sequence,
$a = 4$
$d = 3$

Since you want to find the 37th term, then $n = 37$

${T}_{n} = a + \left(n - 1\right) d$
${T}_{37} = 4 + \left(37 - 1\right) 3$
${T}_{37} = 4 + 36 \times 3$
${T}_{37} = 112$

Aug 2, 2018

${a}_{37} = 112$

#### Explanation:

$\text{these are the terms of an arithmetic sequence}$

$\text{the n th term of an arithmetic sequence is}$

•color(white)(x)a_n=a_1+(n-1)d

$\text{where "a_1" is the first term and d the common difference}$

$d = 7 - 4 = 10 - 7 = 3 \text{ and } {a}_{1} = 4$

${a}_{37} = 4 + \left(36 \times 3\right) = 4 + 108 = 112$