Question

If the number of shot in a triangular pile is to the number of shot in square pile of double the number of courses as 13:175 ;

find the number of shot in each pile.

✔️✔️ quality answer needed✔️✔️
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Answer 1

This is an arithmetic sequence: 1,2,3,4... [counting down from the top of the pile]

The nth term of an arithmetic sequence is

a(n) = a(1) + (n-1)d where a(1) = the 1st term, d = the common difference

In this case a(n) = 1 + (n-1) = n

The sum of the 1st n terms of the sequence is S(n) = (n/2)(a(1) + a(n)) = 105

So S(n) = (n/2)(1+n) = 105

Solve for n:

n^2 + n - 210 = 0

Factor:

(n-14)(n+15) = 0

Take the positive solution, n=14

So there are 14 layers