# Find the 30th term of the arithmetic series 60, 53, 46, 39...

Find the 30th term of the arithmetic series 60, 53, 46, 39...
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Abagail Stephenson
The standard 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
$d={a}_{2}-{a}_{1}={a}_{3}-{a}_{2}=........={a}_{n}-{a}_{n-1}$
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
$⇒{a}_{30}=60+\left(30-1\right)\left(-7\right)=60+\left(29×-7\right)=-143$