1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kvv77 [185]
3 years ago
12

Find the formula for the nth term of the sequence: 0,7,18,33,52​

Mathematics
1 answer:
defon3 years ago
8 0

Answer:

t(n) = 2n² + n - 3

Step-by-step explanation:

<u>Given sequence: </u>

  • 0, 7, 18, 33, 52

Find the formula for nth term t(n)

<h3>Solution</h3>

<u>Sequence is neither arithmetic nor geometric, analyzing:</u>

  • 0, 7, 18, 33, 52

<u>First level difference</u>

  • 7, 11, 15, 19

<u>Second level difference</u>

  • 4, 4, 4

<u>As there are two levels, the formula should be in the form of:</u>

  • t(n) = an² + bn + c

<u>Trying the formula with the known terms:</u>

  • t(1) = 0 ⇒ a+b + c= 0
  • t(2) = 4a + 2b + c = 7 ⇒ 3a + b = 7
  • t(3) = 9a + 3b + c = 18 ⇒ 3(3a+b) + c = 18 ⇒ 21 + c = 18 ⇒ c = -3

<u>Going back to previous equations to find remaining coefficients:</u>

  • t(1) ⇒ a+ b = 3 ⇒ t(2) = 2a + (a+b) = 7 ⇒2a + 3 = 7 ⇒ a= 2 ⇒ b = 1

<u>So the formula becomes:</u>

t(n) = 2n² + n - 3

You might be interested in
What kind of word problem can be solved with a two-variable equation?​
Annette [7]

Answer: Here’s one I made up! Combined, Megan and Kelly worked 60 hours, Kelley worked twice as many hours as Megan. How many hours did they each work? Hope this helps!

5 0
3 years ago
Find the limit of the sequence of partial sums whose general term is <img src="https://tex.z-dn.net/?f=a_n%3D%5Cfrac%7B100%5En%7
nasty-shy [4]

Answer:

0

Step-by-step explanation:

If ∑aₙ converges, then lim(n→∞)aₙ = 0.

Using ratio test, we can determine if the series converges:

If lim(n→∞) |aₙ₊₁ / aₙ| < 1, then ∑aₙ converges.

If lim(n→∞) |aₙ₊₁ / aₙ| > 1, then ∑aₙ diverges.

lim(n→∞) |(100ⁿ⁺¹ / (n+1)!) / (100ⁿ / n!)|

lim(n→∞) |(100ⁿ⁺¹ / (n+1)!) × (n! / 100ⁿ)|

lim(n→∞) |(100 / (n+1)|

0 < 1

The series converges.  Therefore, lim(n→∞)aₙ = 0.

7 0
3 years ago
Simplify: x+4-5x-2 <br><br>A:-5x+2<br>B:-5x-2<br>C:-4x+2<br>D:-4x-2​
mezya [45]

Answer:

C:-4x+2

Step-by-step Explanation:

x + 4 - 5x - 2 \\  = x - 5x + 4 - 2 \\ =   - 4x + 2 \\

5 0
3 years ago
An item is regularly priced at $81. It is on sale for 45% off the regular price. Find the sale price.
Triss [41]

Answer:

44.55

Step-by-step explanation:

Internet said this: "Thus, a product that normally costs $ 81 with a 45 percent discount will cost you $ 44.55, and you saved $ 36.45. You can also calculate how much you save by simply moving the period in 45.00 percent two spaces to the left, and then multiply the result by $ 81 as follows: $ 81 x. 45 = $ 36.45 savings."

Hope this helps∞<3

Let me know if it right or wrong!

3 0
3 years ago
Read 2 more answers
15.1 m<br> 25.5 m<br> 35.7 m<br><br> FIND THE SURFACE AREA OF EACH RECTANGULAR PRISM
bezimeni [28]
Oooooooooooooooooooowqqqqqqqqqqqqqqqqqqqqdddqqqqqqqqqhujkuz 

5 0
3 years ago
Other questions:
  • Growth or decay: 1/2(10)^x
    15·1 answer
  • What is the value of g(9)?
    14·1 answer
  • Find the y-intercept for the parabola defined by
    8·1 answer
  • Examine the following table of points, which are all on a certain line.
    12·1 answer
  • Please answer right away
    6·1 answer
  • Pls help this question bamboozles me and I am now sitting here confused
    6·1 answer
  • What is the range of f(x) = (three-fourths) Superscript x – 4?
    10·1 answer
  • I need help on this and the first person who answer correctly gets a BRANILIST​
    15·1 answer
  • The coordinates of the turning point of the graph of
    15·1 answer
  • Your break even point is 3000 units you make $5 each unit that is your price minus variable coals is $5 what your fixed cost ? U
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!