What is a40 for the arithmetic sequence presented in the table below?

n 8 12
an 60 48

hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference

Lets first get the common difference = d.

Using,
an = a1 +d(n-1)
a8 = a1+ d(8-1)
60 = a1+7d

a12 = a1 + d(12-1)
48 = a1 + 11d

from these 2 equations we will get a1, d

subtracting them, we get
60-48 = 7d-11d = -4d
12 = -4d
d = -3.

and
60 = a1 + 7d = a1 + 7(-3) = a1 -21
a1 = 60+21 = 81.

now a40 = a1 + d(40-1) = 81 + (-3)39
a40 = -36.

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