In an arithmetic sequence where a₁ = 5 and d = 3, what is the 5th term?

To find the 5th term of an arithmetic sequence, you can use the formula for the nth term, which is given by:

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

In this case, we know that the first term ( a_1 ) is 5, the common difference ( d ) is 3, and we want to find the 5th term, where ( n = 5 ).

Substituting the values into the formula, we have:

[ a_5 = 5 + (5 - 1) \cdot 3 ]

[ a_5 = 5 + 4 \cdot 3 ]

[ a_5 = 5 + 12 ]

[ a_5 = 17 ]

This calculation shows that the 5th term of the sequence is indeed 17, confirming that option C is the correct choice. Each term in the sequence increases by 3 from the previous term, creating a consistent pattern that aligns with the arithmetic sequence definition.