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What is the 32nd term of the arithmetic sequence where a1 = –31 and a9 = –119?


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Verified Answer :

MissPhiladelphia

In
order to solve for a nth term in an arithmetic sequence, we use the formula
written as:


an = a1 + (n-1)d


where an is the nth term, a1 is the first value
in the sequence, n is the term position and d is the common difference.


First, we need to calculate for d from the given
values above.  
a1 = -31 and a17 = -119



an = a1 + (n-1)d

-119 = -31 + (9-1)d

d = -11


The 32nd term is calculated as follows:


a32 = a1 + (n-1)d

a32= -31 + (32-1)(-11)
a32 = -372