The second term in an arithmetic sequence is 5 and the fifth term is 68. What is the function?

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Answer 1 · 2017-01-09T00:32:01

The general formula for a term can be written:

#a_n = 21n-37#

The general term of an arithmetic sequence is given by the formula:

#a_n = a+d(n-1)#

where #a# is the initial term and #d# the common difference.

We find:

#3d = (a+4d)-(a+d) = a_5-a_2 = 68-5 = 63#

Dividing both ends by #3# we get:

#d = 21#

Then:

#a_1 = a = (a+d)-d = a_2-d = 5-21 = -16#

So the formula for the general term can be written:

#a_n = -16+21(n-1) = 21n-37#