Question

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

Answer 1

`-143`

Explanation:

The standard `color(blue)"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

`rArra_(30)=60+(30-1)(-7)=60+(29xx-7)=-143`