7, 9, 11, 13 ...

Generalize the pattern by finding an explicit formula for the nth term.

2n + 5

Step-by-step explanation:

the difference between each term is + 2. (therefore, 2n)

so you have to do the opposite to 7 to find the second bit of the sequence.

7 - 2 = 5

2n+5

an = 5 + 2n

Step-by-step explanation:

Each time it increases by the same amount (2), so this is an arithmetic sequence:

an = a₁ + d (n - 1)

Given a₁ = 7 and d = 2:

an = 7 + 2 (n - 1)

an = 7 + 2n - 2

an = 5 + 2n

Check our answer:

n=1: a₁ = 5 + 2 (1) = 7

n=2: a₂ = 5 + 2 (2) = 9

n=3: a₃ = 5 + 2 (3) = 11

n=4: a₄ = 5 + 2 (4) = 13