In an arithmetic sequence, each term is generated by adding a constant difference to the previous term.
For the sequence you provided:
- First term (\(a_1\)): 4
- 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.