#### Question

It is given that 13, 21, 29,..., 165 is an arithmetic sequence.

How many terms are there in the sequence?

Does the sequence contain the 12th term? If yes, find the 12th term of the sequence.

It is given that 13, 21, 29,..., 165 is an arithmetic sequence.

How many terms are there in the sequence?

Does the sequence contain the 12th term? If yes, find the 12th term of the sequence.

Since the series 13, 21, 29,..., 165 is an arithmetic sequence, let d be the common difference of the sequence

d= 21-13=29-21=8

Using the formula for general terms of an arithmetic sequence

a_n = a_1+(n-1)d

165 = 13+8(n-1)

160 =8n

n =20

Hence, there are 20 terms in the sequence

Yes, there are 12th term in the sequence

a_{12}=a_1+11d

=13+11\times 8

=101