how many terms are there in this sequence?

Question

20;23;26;29;...;101

Answer 1

This is an arithmetic progression (AP).

The nth term can be written 20+3(n-1) because the common difference 3 is added one less than the number of terms in the series. For example, the 3rd term (26), has n=3, so 20+3×(3-1)=20+6=26.

So if 20+3(n-1)=101, 20+3n-3=101, 3n=101-20+3=84, making n=84/3=28. So 101 is the 28th term, and there must be 28 terms in the series.