In the sequence 5,19/3,23/3 which term is 65?

Question

Steps on how to do this problem.

Answer 1

60=n*4/3
180=4n
45=n
Therefore, it will be the 46th term in this expansion.

Answer 2

Note that this is an arithmetic sequence. An arithmetic sequence has a common difference between the terms. Also note that the difference between each term is 4/3 (5+4/3=19/3, 19/3+4/3=23/3).

The form of an arithmetic sequence is:

a+(n-1)d, where a is the first term, d is the common difference, and n is the number of the term. a=5, d=4/3.

5 + (n-1)(4/3) = 65
(n-1)(4/3) = 60
n-1 = 45
n= 46

It is the 46th term.