Sample Problem

An arithmetic sequence begins as follows: 1, 6, 11 …

1)      What is the 20th term of the sequence?

2)      Which term of the sequence is 141? th term


1)      The arithmetic sequence has 1st term 1 and common difference 5. The 20th term is formed by adding the common difference 19 times to the 1st term. So the 20th term is 1 + 19 × 5 = 96.

2)      By subtracting the first term from 141 and dividing by the common difference, we find the number of times the common difference is added to the first term to get the last term, in other words the number of terms after the first term up to 141. Adding 1 to this result accounts for the presence of the first term and therefore gives the number of terms from the first term to 141, which lets us know which term of the sequence 141 is. So 141 is the (141 – 1) /5 + 1 = 29th term.