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For a given arithmetic sequence, the 75th term, a75, is equal to 342, and the 4th term, 24, is equal to - 13.

nd
Find the value of the 32
term, 232

User The Pjot
by
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1 Answer

3 votes

Answer:

The 32th term is 127.

Explanation:

Arithmetic sequence:

In an arithmetic sequence, the difference between consecutive terms is always the same. The general equation for an arithmetic sequence is given by:


a_n = a_1 + (n-1)d

In which d is the common difference.

It can also be written as:


a_n = a_m + (n - m)d

75th term is equal to 342, and the 4th term, 24, is equal to - 13.

This means that
a_4 = -13, a_75 = 342. We use this to find d. So


a_(75) = a_4 + (75 - 4)d


342 = -13 + 71d


71d = 355


d = (355)/(71)


d = 5

Find the value of the 32th term:


a_n = a_m + (n - m)d


a_(32) = a_(4) + (32 - 4)d


a_(32) = -13 + 28(5) = -13 + 140 = 127

The 32th term is 127.

User Jesper Madsen
by
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