Explanation
To find the 21st term of the sequence \(-3, 2, 7, \ldots\), first determine the common difference of the arithmetic sequence.
1. Find the Common Difference:
\[
\text{Common difference} = 2 - (-3) = 5
\]
2. Use the Formula for the \(n\)th Term of an Arithmetic Sequence:
\[
a_n = a_1 + (n - 1) \cdot d
\]
where \(a_1\) is the first term, \(d\) is the common difference, and \(n\) is the term number.
For this sequence:
\[
a_1 = -3
\]
\[
d = 5
\]
\[
n = 21
\]
3. Substitute the Values into the Formula:
\[
a_{21} = -3 + (21 - 1) \cdot 5
\]
\[
a_{21} = -3 + 20 \cdot 5
\]
\[
a_{21} = -3 + 100
\]
\[
a_{21} = 97
\]
Thus, the 21st term of the sequence is 97.