Thread: Arithmetic Series
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Old May 2nd, 2008, 06:41 AM
Soroban Soroban is offline
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Hello, stones44!

Quote:
So there is wall.
The top has 1 brick, then the next row has 3 bricks, then 5 bricks, etc.
There are 2500 bricks in the wall.
How many rows are there?

Without a formula? . . . Then a child can do it!

Just start adding: .1 + 3 + 5 + 7 + 9 + \hdots . until you reach 2500.

Then count up the number of numbers you added.
. . . I'll wait in the car . . .



Formula for the sum of the first n terms of an arithmetic series:
. . S_n \;=\;\frac{n }{2}[2a + (n-1)d]

We have: .first term, a = 1 . . . common difference, d = 2

We know: .S_n = 2500 . . . and we want n.


So we have: .2500 \:=\:\frac{n}{2}[2(1) + (n-1)2] \quad\Rightarrow\quad 2500 \:=\:\frac{n}{2}(2n)\quad\Rightarrow\quad n^2 \:=\:2500

Therefore: .n \:=\:50 . . . There are 50 rows.
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