Question

find the indicated term in each arithmetic sequence.
a_(32) for 4, 7, 10, 13

Answer 1

In an arithmetic sequence, each term is generated by adding a constant difference to the previous term.

For the sequence you provided:

1. First term (\(a_1\)): 4
2. Common difference (\(d\)): 7 - 4 = 3

The general formula for the \(n\)-th term of an arithmetic sequence is:

\[
a_n = a_1 + (n-1) \cdot d
\]

To find the 32nd term (\(a_{32}\)), we can substitute \(a_1\), \(d\), and \(n = 32\) into the formula:

\[
a_{32} = 4 + (32 - 1) \cdot 3
\]
\[
a_{32} = 4 + 31 \cdot 3
\]
\[
a_{32} = 4 + 93
\]
\[
a_{32} = 97
\]

Thus, the 32nd term of the sequence is **97**.