Question

The sum of 40 numbers in an arithmetic sequence is 8000. If the first number is the sequence is 83, what is the last number?

Answer 1

`317`

Explanation:

In an arithmetic sequence the difference between consecutive members is constant. Therefore the sequence is
`83, 83+d, 83+2d,.....83+39d`

The `i`th member is `83+(i-1)d`

As shown on Arithmetic Sequences the formula for the sum of members is
`sum_0^(n-1) (a+kd) = n/2*(2a+(n-1)d)`

In this case
`sum_0^39 = 40/2*(2*83+39*d) = 8000`
`166+39d = 400`
`39d= 234`

`d=234/39 = 6`

The `40`th number is therefore `83 +39*6 = 317`