# What is the 32nd term of the arithmetic sequence where a1 = 12 and a13 = -60?

The 32nd term of the arithmetic sequence
where a1 = 12 and a13 = -60 is -174.
The general nth term of an arithmetic series
with initial term a1 and common difference d
is given by an = a1 + (n – 1)d.
a1 = 12
a13 = 12 + (13 – 1)d
a13 – 12d = 12
12d = a13 – 12
12d = -60 – 12
d = -6
a32
= a1 + (n – 1)d
= 12 + 31*(-6)
= -174

A31=-174

Source(s): Matherician

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