Answer:
- AP
- tₙ = (n-2)k² + (2n - 3)k + n
Step-by-step explanation:
<u>Given sequence:</u>
- -k² - k + 1, k + 2, k² + 3k + 3, 2k² + 5k + 4, ...
We can see apart from the second term all terms are 2nd degree trinomial so it is not a GP.
Let's find the difference: to determine if it is a AP:
- k + 2 - (-k² - k + 1) = k + 2 + k² + k -1 = k² + 2k + 1
- k² + 3k + 3 - (k + 2) = k² + 3k + 3 - k - 2 = k² + 2k + 1
- 2k² + 5k + 4 - (k² + 3k + 3) = 2k² + 5k + 4 - k² - 3k - 3 = k² + 2k + 1
As we see the difference is common and it confirms the sequence is AP.
<u>First term is </u>
<u>Common difference is </u>
<u>nth term is:</u>
- tₙ = a₁ + (n-1)d
- tₙ = -k² - k + 1 + (n-1)(k² + 2k + 1) =
- -k² - k + 1 + (n-1)k² + (n-1)*2k + n-1 =
- (n-2)k² + (2n - 3)k + n
Answer:
Step-by-step explanation:
<u>To make the given piecewise function continuous we need:</u>
- ax² - b = 6 and 5ax + b = 6 at x = 1
<u>It gives us the system:</u>
- a(1²) - b = 6 ⇒ a - b = 6
- 5a(1) + b = 6 ⇒ 5a + b = 6
<u>Sum of the two:</u>
- a - b + 5a + b = 6 + 6
- 6a = 12
- a = 2
<u>Then b is:</u>
Answer: $358.8 to the nearest tenth
Step-by-step explanation:
Compound interest is calculated by Where: A = P(1 + r)t
Where P= 300, r= 12% = 0.12, t= 1.5 years
Slot in the figures
300 (1 + 0.12) 1.5
300 (1.12) 1.5
300x 1.12
336e1.12
A = $ 358.84
Answer:
43
Step-by-step explanation:
D) 48
2 packs of plates is 48 plates and 3 packs of cups os 48 plates.