# How do i find the tenth term if the first term is 12 and common difference is 3?

Feb 4, 2018

${a}_{10} = 39$

#### Explanation:

$\text{for an "color(blue)"arithmetic sequence}$

$\text{the nth term is }$

•color(white)(x)a_n=a+(n-1)d

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

$\Rightarrow {a}_{10} = 12 + \left(9 \times 3\right) = 12 + 27 = 39$

Feb 4, 2018

The ${n}^{t h}$ term of an Arithmetic Progression is given by,
${a}_{n} = a + \left(n - 1\right) d$

For the ${10}^{t h}$ term, with the given details,
n=10 ; a=12; d=3

${a}_{10} = 12 + \left(9\right) 3$
${a}_{10} = 12 + 27$
${a}_{10} = 39$

So, the tenth term is 39 !:)