Find the number of terms in the sequence or the sum of the sequence as requested.
-Find the number of terms in the following arithmetic sequence. 8, 11, 14, 17, . . ., 89
A)28
B)30
C)81
D)84

Question

Quizplus · Accepted Answer

The sequence is an arithmetic sequence with a common difference of 3 (since 11 - 8 = 3, 14 - 11 = 3, etc.). To find the number of terms, use the formula for the nth term of an arithmetic sequence: $a_n = a_1 + (n - 1)d$, where $a_n$ is the nth term, $a_1$ is the first term, $d$ is the common difference, and $n$ is the number of terms. Plugging in the values, we get $89 = 8 + (n - 1)3$. Solving for $n$, we find $n = 28$.

Find the Number of Terms in the Sequence or the Sum