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Zarrin [17]
3 years ago
8

Find the value of 1×4+2×5+3×6......n×(n+3)​

Mathematics
1 answer:
Arada [10]3 years ago
3 0

Answer:

n(n+1)(n+5)/3

Step-by-step explanation:

there is no value, as we don't know n.

but we can create a summary formula/ function definition :

this is the sum for k = 1 to n of k×(k+3)

k×(k+3) = k² + 3k

so, the overall sum splits into the sum of k² for k=1 to n, and the sum of 3k for k=1 to n.

and the sum of 3k is 3 times the sum of k for k=1 to n.

Σk² for k=1 to n = [n(n+1)(2n+1)]/6

Σk for k=1 to n = n(n+1)/2

3×Σk for k=1 to n = 3×n(n+1)/2

so, we have a function formula

n(n+1)(2n+1)/6 + 3n(n+1)/2 = n(n+1)(2n+1)/6 + 9n(n+1)/6 =

= n(n+1)(2n+1+9)/6 = n(n+1)(2n+10)/6 = n(n+1)(n+5)/3

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If n>4 then n/4>7
Hope I helped :)

8 0
3 years ago
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dangina [55]

Answer:  The correct option is

(E) 80,000.

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We are to find the number of gallons of water that the tank hold when filled to capacity.

Let the tank can hold x gallons of water when filled to capacity.

Then, according to the given information, we have

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4 0
3 years ago
Write a situation that could be represented by the equation y=15x-3
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A tree grows at a rate of 15 inches per year.  However, three inches were chewed off by quasi-sadistic bunnies the first year it was planted.  Fortunately, the bunnies were frightened off by the garden gnomes, and did not return.  As a result the tree was able to grow unencumbered for the rest of its life.
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Answer:

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Step-by-step explanation:

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6 0
2 years ago
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