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

1)
What
is the 20^{th} term of the sequence?

2)
Which
term of the sequence is 141? ^{th} term

1)
The
arithmetic sequence has 1^{st} term 1 and common difference 5. The 20^{th}
term is formed by adding the common difference 19 times to the 1^{st}
term. So the 20^{th} 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 = 29^{th}
term.