Answer:
→ (a)
Step-by-step explanation:
We need to evaluate g(n - 7), where
Replace x by (n - 7) to evaluate it
∵ x = (n - 7)
∴
→ Let us find (n - 7)²
∵ (n - 7)² = (n - 7)(n - 7) = (n)(n) + (n)(-7) + (-7)(n) + (-7)(-7)
∴ (n - 7)² = n² + (-7n) + (-7n) + 49 = n² + -14n + 49
∴ (n - 7)² = n² - 14n + 49
→ Find 7(n - 7)
∵ 7(n - 7) = 7(n) - 7(7)
∴ 7(n - 7) = 7n - 49
→ Now let us write then in the form above
∵
→ Add the like terms in the numerator
∴
The correct answer is (a)
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