#### Question

Find an equation for the general term of the given arithmetic sequence and use it to calculate its 75^{th} term: 8,5,2,-3,−6,…

Begin by finding the common difference,

d=5−8=−2

Next find the formula for the general term, here a_1=8 and d=−3.

a_n=a_1+(n-1)d

=8+(n-1)(-3)

= -3n+11

Therefore, a_n=-3n+11 and the 75^{th} term can be calculated as follows:

a_{75}=11-3\times 75 =214