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.
Answer
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