A series contains 18 numbers and has a sum of 4,185. The last number of the series is 275. What is the first number?

The sum of arithmetic series is given by:

Sn=n/2 (a1+an)

where:

n=number of terms

a1=first term

an=nth term

but

n=18, an=275, Sn=4185

plugging the values in the formula we get:

4185=18/2 (a1+275)

simplifying this we get:

4185=9 (a1+275)

dividing through by 9 we get:

465=a1+275

thus

a1=465-275

a1=190

Answer: first number is 190