Hello,
I suppose you want the 4 numbers.
Let's call the numbers
I suppose you want the 4 numbers.
Let's call the numbers
I need to know how to do these so someone please work them out ASAP. Thank you.
1 answer:
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Answer:
f(N) = ((N+1)^2 -((N+1) mod 2))/4
Step-by-step explanation:
The number of blocks is the sum of an arithmetic sequence with a common difference of -2. That sum is the product of the average number of blocks in a row and the number of rows.
<u>For N odd</u>:
The number in the base row is N, and the number in the top row is 1. The average number of blocks in a row is (N+1)/2. The number of rows is (N+1)/2, so the total number of blocks in the design is ...
f(N) = (N+1)^2/4
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<u>For N even</u>:
The number in the base row is N, and the number in the top row is 2. The average number of blocks in a row is (N+2)/2. The number of rows is N/2, so the total number of blocks in the design is ...
f(N) = ((N+1)^2 -1)/4
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<u>Combined formula</u>:
The difference between these formulas is an additive value of -1 when N is even. There are some different ways that an even/odd function can be written. One is ...
even(N) = (N+1) mod 2 . . . . . 1 when N is even; 0 otherwise
another might be ...
even(N) = (1 +(-1)^N)/2
So, for any integer N, the formula for the number of blocks in the design could be ...
f(N) = ((N+1)^2 -((N+1) mod 2))/4
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A graph of this function for 1 to 10 blocks on the first row is attached.
