Many dots

Algebra Level 1

On day 1, I have one dot. On day 2, I add two dots. On day 3, I add three dots. On day 4, I add four dots...

How many dots do I have on day 30 after adding the 30 dots?


The answer is 465.

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David Pilling by David Pilling , 18, USA

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3 solutions

Hung Woei Neoh
May 15, 2016

1 + 2 + 3 + … + 30 = ∑ n = 1 30 n = ( 30 ) ( 30 + 1 ) 2 = 15 ( 31 ) = 465 1+2+3+ \ldots+ 30\\ =\displaystyle \sum_{n=1}^{30} n\\ =\dfrac{(30)(30+1)}{2}\\ =15(31)\\ =\boxed{465}

3 Helpful 1 Interesting 1 Brilliant 1 Confused

Nice (+1) :)

Ashish Menon - 5 years, 1 month ago
Jonas Bach
May 29, 2016

Since 1+30=31 And 29+2=31 ... 15+16=31 Therefore, the solution is 31*15=465

You can do this with any number Let your number be n and all numbers added up until that number be f Then for even numbers: n+1 n/1and for uneven numbers_ n+1 n-1/2+n+1/2

1 Helpful 0 Interesting 0 Brilliant 0 Confused
David Pilling
May 15, 2016

The answer is 1 + 2 + 3 + . . . + 30 = 465 1+2+3+ ... + 30 = \boxed{465}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

I have edited the problem. I believe it is okay.

Chew-Seong Cheong - 5 years, 1 month ago

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