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The 31st term of an arithmetic sequence is 496. If the common difference is 16, what is the second term?

The 31st term of an arithmetic sequence is 496. If the common difference is 16, what-example-1

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Take into account that the general expression for the nth term of a arithmetic sequence is given by:


a_n=a_1+(n-1)d

where, for this case:

an: 31st term = 496

n = 31

d: common difference of the sequence = 16

a1 = first term = ?

Solve the previous equation for a1, replace the values of the parameters and simplify:


\begin{gathered} a_1=a_(31)-(31-1)16 \\ a_1=496-(31)16 \\ a_1=0 \end{gathered}

Then, the nth term can be written as follow:


a_n=(n-1)d

and the second term is given by (n = 2):


a_2=(2-1)16=16

Hence, the second term is 16

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