#### Question

It is given that 49,..., 17 is an arithmetic sequence. If there are 25 terms in the sequence, find the common difference of the sequence.

Since the series 49,..., 17 is an arithmetic sequence, let d be the common difference.

Using the formula for the general terms for an arithmetic sequence

a_{17}=a_1+(17-1)d

17 = 49+16d

-32=16d

d= -2

Now we get find the common difference of the sequence as -2.