In a triangular pile of logs, the top row contains one log. Each row below the top row contains one log more than the row above it. If the bottom row contains 435 logs, how many logs are in the pile?

Question

In a triangular pile of logs, the top row contains one log. Each row below the top row contains one log more than the row above it. If the bottom row contains 435 logs, how many logs are in the pile?

Please answer in an organized and neat/easy to read format. And please only include the information that would be understood by a Grade 11. Thank you :)

Answer 1

105,830 logs total.

why.

if there is a sum, S=1+2+3+4+..+n

then S=n(n+1)/2,,,,,,it is kind of useful and is proven by induction proof

problem is to find S=1+2+3+...+435

435*436/2=105,830.

Answer 2

1,2,3, ...,435 is an AP with d=1, a1=1

an = a1+d(n-1) = 1+1(434) = 435

sum of n terms

= n(n+1)/2 = 435(436)/2 = 435(218) = 94,830 by Gauss' formula= sum of n integers from 1 to n

or

sn + (n/2)(a1+an) = 435(1+435)/2 = 435(436)/2 = 435(218) = 94,218