Question

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

Answer 1

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