Question

How many terms are in the arithmetic sequence 1313, 1616, 1919, ……, 7070, 7373?

Answer 1

The formula in getting the arithmetic sequence:
an = a1 + (n – 1)d.

We can substitute the values in order for us to know how many terms the sequence has.

an = 7373
a1 = 1313
d = 303

an = a1 + (n – 1)d
7373 = 1313 + (n-1) 303
7373 = 1313 + 303n - 303
-303n = 1313 - 303 - 7373
303n = -1313 + 303 + 7373
303n = 6363
n = 21

So, there are 21 terms in the sequence given.