Answer:
a(n) = 3n - 2.
Step-by-step explanation:
The nth term of an arithmetic sequence = a1 + d(n - 1) where a1 = the first term and d = the common difference.
So here we have:
a3 = 7 = a1 + 2d
a5 = 13 = a1 + 4d
Rewriting:
a1 + 4d = 13
a1 + 2d = 7
Subtracting, we eliminate a1:
2d = 6
d = 3
and a1 = 7 - 2(3)
= 1.
So our equation we can use to find any term is
a(n) = 1 + 3(n - 1)
a(n) = 1 + 3n - 3
a(n) = 3n - 2 (answer).
Checking :
3rs term = 3(3) - 2 = 7.
5th term = 3(5) - 2 = 13.
First term = 3(1) - 2 = 1.
