Question

What are the first four terms in tn=3n+2

Answer 1

For this question we are looking at arithmetic sequences.  A sequence is any set of numbers in a particular order.  An arithmetic sequence is a specific type of sequence where the difference between 2 consecutive terms is constant.  The difference is called the common difference.  In your problem...

t_n = 3n + 2

we need to find the common difference, then we can find the 1st four terms. Find the 1st term by replacing n with 1.

t_1 = 3(1) +2
t_1 = 3 +2 = 5

Find the second term by replacing n with 2

t_2 = 3(2) + 2 = 8

and so on

t_3 = 3(3) + 2 = 11

t_4 = 3(4) + 2 = 14

The 1st 4 numbers in the sequence are 5,8,11, and 14.

You can see the common difference is d=3.  You could plug any number into the equation to find that number in the sequence.  For example, the 100th number in the sequence would be

t_100 = 3(100) + 2 = 302