Question

Determine the nth term for each of the following sequences: 2,5,8,11,14,..

Answer 1

To determine the nth term, we must create a function.

f(n) = 1st term + common difference (n - 1)

n = term you are looking for
1st term = 1st number in the sequence
common difference = the difference between two consecutive numbers in the sequence.

based on the above sequence, the 1st term is 2, its common difference is 3.

f(n) = 2 + 3(n-1)

Assuming we are looking for the 5th term
f(5) = 2 + 3(5-1)
       = 2 + 3(4)
       = 2 + 12
f(5) = 14   as you can see in the above sequence 14 is the 5th term.

For any other value of the nth term, simply substitute n by the number of the term and solve the equation.