a triangular wall is made up of one brick on the top layer, 2 bricks on the second then 3 bricks on the third.... if there are 171 bricks altogether, how many layers are there?

Question

jamesj · Answer

So you want to know: what is an expression for
1 + 2 + 3 + .... + n.  Suppose that expression is S(n).

Then the question is for what value of n is S(n) = 171 ?

jamesj · Answer

Do you know the expression for S(n)?

anonymous · Answer

but I substituted the values into the general equation of Sn for arithmetic sequences and the answer was 300 something which is impossible, could you please show me how to find n?

anonymous · Answer

So S(n) = n(n+1)/2, hence we want n such that
n(n+1)/2 = 171
n^2 + n = 342

Now solve  n^2 + n - 342 = 0

jamesj · Answer

Right.  This will give you a negative value and a positive value.

anonymous · Answer

but the answer is supposed to be 18

jamesj · Answer

Yes ... that is the positive solution.  Obviously the negative solution here is not meaningful.

anonymous · Answer

oh woops sorry stupid question, haha, I though my answer was either 342 or 341

jamesj · Answer

ok