Consider the arithmetic series 7 + 19 + 31 + 43 + 55 + pr004-1.jpg.

Question

a) How many terms are less than 1000? (3 marks - show your work)
b) How many terms are less than 2000? (3 marks - show your work)

Answer 1

We have
a=7
d=12

So, when does Tn exceed 1000?

Tn = 7+12(n-1) = 12n-5
12n-5 < 1000
12n < 1005
n < 83.75
So, the first 83 terms are less than 1000

Similarly for 2000