Arithmetic Sequences

Question

If the third term of an arithmentic sequence is 1 and the eighth term is -14, what is the twelfth term?

Answer 1

Use the formula an = a1 + (n-1)d to solve this problem.

First we need to find the difference (d).

Here an is the 8th term, and 1 is the 3rd term and n = 6 (the number of terms 3, 4, 5, 6, 7, 8).

So -14 = 1 + 5*d

and d = -3

Now we can use the same formula to find a12:

a12 = a8 + (n-1) * d. We know d = -3 and n = 5 (the number of terms 8, 9, 10, 11, 12) and a8 = -14.

Thus a12 = -14 + -12 = -26