Consider the arithmetic sequence presented in the table below. n 4 37 and an 16 115 what is the first term, a1, and the 22nd term of the sequence?

If I'm reading this correctly, the table is telling you that and .

Because the sequence follows an arithmetic progression, there is a common difference between terms such that



You can solve for explicitly in terms of the first term by recursively substituting the right side:






Let's first find the common difference. You have






Substituting in the terms of the sequence that you know, you get



Now you can find the first term:



and the 22nd term:

The equation is y=17(7)+600 and it equals 717