Question

find a formula for the nth term in this arithmetic sequence:
a₁ = 9, a₂ = 13, a₃ = 17, a₄ = 21, ...
aₙ = ?n +

Explanation:

Step1: Find the common difference (d)

In an arithmetic sequence, the common difference \( d \) is the difference between consecutive terms. Let's calculate \( d \) using \( a_2 - a_1 \).
\( d = a_2 - a_1 = 13 - 9 = 4 \)

Step2: Recall the formula for the nth term of an arithmetic sequence

The formula for the nth term of an arithmetic sequence is \( a_n = a_1 + (n - 1)d \). We can also rewrite this in the form \( a_n = dn + (a_1 - d) \) to match the given form \( a_n = [?]n + [\square] \).

Step3: Substitute \( a_1 = 9 \) and \( d = 4 \) into the rewritten formula

First, we know \( d = 4 \), so the coefficient of \( n \) is \( 4 \). Now we find the constant term: \( a_1 - d = 9 - 4 = 5 \). So the formula for the nth term is \( a_n = 4n + 5 \).

Answer:

\( a_n = 4n + 5 \) (So the coefficient of \( n \) is \( 4 \) and the constant term is \( 5 \))