# What is the 30th term of the arithmetic series 60, 53, 46, 39..?

Jun 2, 2016

$- 143$

#### Explanation:

The standard $\textcolor{b l u e}{\text{Arithmetic sequence}}$ has terms

a ,a+d ,a+2d ,a+3d , ............ , a+(n-1)d

where a is the 1st term , d is the common difference and
a+(n-1)d is the nth term

$d = {a}_{2} - {a}_{1} = {a}_{3} - {a}_{2} = \ldots \ldots . . = {a}_{n} - {a}_{n - 1}$

here a = 60 , d = 53 - 60 = 46 - 53 = -7

To find the 30th term use the nth term with n = 30 , a = 60
and d = -7

$\Rightarrow {a}_{30} = 60 + \left(30 - 1\right) \left(- 7\right) = 60 + \left(29 \times - 7\right) = - 143$