A student uses the explicit formula an = 5+3 (n-1) for the sequence 3,8,13,18,23, ... to find the 12th term. Explain the error the student made.

Formula should be an = 3 + 5 (n - 1)

The 12th term = 3 + 5 (12 - 1) = 58

Step-by-step explanation:

Let's find the value of the first term using the given formula:-

n = 1 is plugged into the formula:-

a1 = 5 + 3 (1 - 1)

= 5 + 3 (0)

= 5

This gives the wrong value (it is 3) so the formula is incorrect.

If we study the sequence we see that the common difference is 8-3 = 13 - 8 = 5 and the first term is 3.

The student has confused the first term with the common difference

The correct formula is an = 3 + 5 (n - 1)