Answer:
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
The pattern represents the arithmetic progression and the explicit formula for the nth term is a(n) = 2n + 5
It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have a sequence:
7, 9, 11, 13…
The above pattern represents the arithmetic progression.
The first term a = 7
Common difference d = 2
nth term:
a(n) = 7 + (n - 1)(2)
a(n) = 2n + 5
Thus, the pattern represents the arithmetic progression and the explicit formula for the nth term is a(n) = 2n + 5
Learn more about the sequence here:
brainly.com/question/21961097
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