Question

How many terms are in the arithmetic sequence –27, –16, –5, …, 292?

Hint: a_n=a_1+d(n-1) , where a_1 is the first term and d is the common difference

Answer 1

a(n)=a(1)+d(n-1)
in this case, a(n)=292, a(1)=-27, d=-16-(-27)=11
292=-27+11(n-1)
11(n-1)=319
n-1=29
n=30
there are 30 terms.