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.

#### Question

#### Answer

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.