Posted by Angel on Monday, September 19, 2011 at 12:36am.
An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.
If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the nth term of the sequence is given by:
an = a1 + ( n - 1 ) * d
In this case:
a13 = 12 + ( 13 - 1 ) * d
- 60 = 12 + 12 * d
- 60 - 12 = 12 d
- 72 = 12 d Divide both sides with 12
- 72 / 12 = 12 d / 12
- 6 = d
d = - 6
an = a1 + ( n - 1 ) * d
a32 = 12 + ( 32 - 1 ) * ( - 6 )
a32 = 12 + 31 * ( - 6)
a32 = 12 + ( - 186 )
a32 = 12 - 186
a32 = -174
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