We are given:
The nth term of the sequence 3, 10, 17, 24, ... is an + b
To determine the values of a and b, let's examine the terms we have:
n = 1: 3 = a(1) + b
n = 2: 10 = a(2) + b
Subtracting the first equation from the second:
10 - 3 = 7 = a(2-1) = a
So a = 7
Plugging this back into the first equation:
3 = 7(1) + b
3 = 7 + b
b = -4
Therefore, the values of a and b are:
a = 7
b = -4
So the nth term of the sequence is:
an + b = 7n - 4