To find the 90th term of the sequence \(17, 21, 25,\) we first identify the pattern of the sequence.
Notice that the sequence appears to have a constant difference between consecutive terms:
- \(21 - 17 = 4\)
- \(25 - 21 = 4\)
The common difference is \(4\). This indicates that the sequence is an arithmetic sequence.
In an arithmetic sequence, the \(n\)th term can be calculated using the formula:
\[ a_n = a_1 + (n - 1) \cdot d \]
where:
- \(a_n\) is the \(n\)th term,
- \(a_1\) is the first term,
- \(d\) is the common difference, and
- \(n\) is the term number.
In this sequence:
- \(a_1 = 17\)
- \(d = 4\)
Now, substituting \(n = 90\) into the formula:
\[ a_{90} = 17 + (90 - 1) \cdot 4 \] \[ a_{90} = 17 + 89 \cdot 4 \] \[ a_{90} = 17 + 356 \] \[ a_{90} = 373 \]
Thus, the 90th term of the sequence is 373.
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