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
-3x+25=40. You want to isolate x so you have to subtract 25 from both sides. -3x=15. We then want x to be isolated so we have to divide both sides by -3 to make x by itself. x=-5. Therefore, x=-5.
