Adding Odd Numbers

Geometry Level 1

$1 + 3 + 5 + 7 + 9+ 11 + 13 + 15 + 17 = \, ?$

7^2

8^2

9^2

10^2

2 solutions

Rakshit Pandey
May 27, 2016

$1^2 = 1$
$2^2 = 4 = 1+3$
$3^2 = 9 = 1+3+5$
$4^2 = 16 = 1+3+5+7$

The pattern is quite clear

$n^2 = 1+3+5+7+\ldots+(2n -1)$

Using this pattern, sum of first 9 odd numbers is $9^2$ .

@Chung Kevin You forgot to write $9$ in your series. Kindly fix that to avoid confusion.

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Calvin Lin Staff - 5 years ago

I counted the numbers and entered $8^2$ :(

A Former Brilliant Member - 5 years ago

Bad luck buddy. I hope @Chung Kevin fixes this soon.

Rakshit Pandey - 5 years ago

Sorry. I've edited the question. ;)

Chung Kevin - 5 years ago

Ashish Menon
May 28, 2016

$1,3,5,7, \cdots,17$ follow the arithmetic progression with first term $1$ , common difference $2$ and last term $17$ . There are $9$ terms in this sequence. So, the sum of the terms of this AP is $\dfrac{9}{2} × \left(1 + 17\right) = 9 × 9 = \color{#69047E}{\boxed{9^2}}$ .

Adding Odd Numbers

2 solutions

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