Question

What is a40

a
40
of the arithmetic sequence for which a8=60
a
8
=
60
and a12=48
a
12
=
48
?

Answer 1

9514 1404 393

Answer:

-36

Explanation:

Using the expression for the general term, you can fill in the known values and solve for the parameters of the sequence.

an = a1 +d(n -1)

a8 = a1 + d(8 -1) = 60

a12 = a1 + d(12 -1) = 48

The difference of these equations is ...

(a1 +7d) -(a1 +11d) = (60) -(48)

-4d = 12

d = -3

Substituting into the first equation, we have ...

a1 +7(-3) = 60

a1 = 81 . . . . . . . . . add 21

Then the 40th term is ...

a40 = 81 -3(40 -1) = 81 -117

a40 = -36