Question

In a list of 200 numbers,each number after the first is 4 more then the number that comes before it.What is the difference between the first and the last number on this list?

Answer 1

Let a₁ = the first number.

Because each number is 4 more than the number before it, the list of numbers forms an arithmetic sequence with a common difference of d = 4.

The n-th term is

`a_(n) = a_(1)+(n-1)d`

The 200-th term is
a₂₀₀ = a₁ + (200 - 1)*4
= a₁ + 796
a₂₀₀ - a₁ = 796

Because a₂₀₀ is the last number on the list, the difference between the first and the last number on the list is 796.

Answer: The difference is 796.