Question

How many poles will be in a pile of telephone poles if there are 30 in the bottom layer, 29 in the second, and so on, until there is one in the top layer?

Answer 1

`465`

Explanation:

Given: a triangle full of telephone poles with 30 at the bottom, with each consecutive row decreasing by 1 until you have 1 pole at the top.

The answer to this question can be done simply by adding `30 + 29 + 28 + 27 + 26 + 25 + ... + 2 + 1 = 465`

This problem can also be done by summations :

`sum_(i=1)^n i = 1 + 2 + 3 + ... + 29 + 30 = 465`

Using a TI-84:

2nd STAT right arrow MATH 5 . `" "=> "sum"(`

2nd STAT right arrow OPS 5 . `" "=> "sum"("seq"(`

Then type in the equation (use `x` for `i`), then a comma, then the variable used, a comma, the start value, a comma, then the end value, comma, then the step increment (`1`):

`"sum"("seq"(x, x, 1, 30, 1))` ENTER `" "465`

A 4th way is to know that

`sum_(i=1)^n i = (n(n+1))/2 = (30 * 31)/2 = 465`