An interior painter is painting a wall that is 8 feet by 14 feet. He needs to determine how much paint he will need for the job.
1 answer:
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Answer:
3n² + 5n - 2
Step-by-step explanation:
<u>Given sequence</u>:
6, 20, 40, 66, 98, 136, ...
Calculate the <u>first differences</u> between the terms:
As the first differences are not the same, calculate the <u>second differences:</u>
As the <u>second differences are the same</u>, the sequence is quadratic and will contain an n² term.
The <u>coefficient</u> of the n² term is <u>half of the second difference</u>.
Therefore, the n² term is: 3n²
Compare 3n² with the given sequence:
The second operations are different, therefore calculate the differences <em>between</em> the second operations:
As the differences are the same, we need to add 5n as the second operation:
Finally, we can clearly see that the operation to get from 3n² + 5n to the given sequence is to subtract 2.
Therefore, the nth term of the quadratic sequence is:
3n² + 5n - 2
<em>Golden ratio, also known as the golden section, golden mean, or divine proportion, in mathematics, the irrational number (1 + Square root of√5)/2, often denoted by the Greek letter ϕ or τ, which is approximately equal to 1.618.</em>