# What is the 33rd term of this arithmetic sequence 12, 7, 2, -3, -8, …?

Aug 21, 2016

${T}_{33} = - 148$

#### Explanation:

The general term for any AP is given by ${T}_{n} = a + \left(n - 1\right) d$

We can get all the information we need from the given terms:

$a = 12$
$d = - 5 \text{ the values are decreasing and the terms differ by 5}$
$n = 33 \text{ we are asked for the 33rd term, } {T}_{33}$

${T}_{33} = 12 + \left(32\right) \times \left(- 5\right)$

${T}_{33} = - 148$