Arithmetic Sequence

Question

Bricks are stacked like the following. In the example shown, the height of the stack is 4. How many bricks in total are needed to make a stack of height 20?

 

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Answer 1

you have 1 brick over 2 bricks over 3 bricks over 4 bricks and so on...

you want the sum of the first 20 counting numbers

1+2+3+4+5+...+16+17+18+19+20= ??

there are many ways to solve this...

basically you are looking for the 20th triangular number

1

1+2=3

1+2+3=6

1+2+3+4=10

and so on...

20(20+1)/2=20(21)/2=210

using the formula for the sum of an arithmetic sequence...

S(20)=(20/2)(2*1+[20-1]1)

S(20)=10(2+19)

S(20)=10(21)

S(20)=210

using logic and simple arithmetic...

1+2+3+4+5+...+16+17+18+19+20= ??

1+20=21

2+19=21

3+18=21

4+17=21

5+16=21

and so on...

there are 10 sums of 21 (20 numbers grouped by 2's)

10*21=210