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
vazorg [7]
3 years ago
7

I need help on this questions. These sequences are hard.​

Mathematics
1 answer:
marissa [1.9K]3 years ago
4 0

Step-by-step explanation:

1. "List the first 9 terms of the sequence defined recursively by

Sₙ = Sₙ₋₂ · (Sₙ₋₁ − 1)

with S₁ = 2 and S₂ = 3"

The first two terms are provided.  To find the third term, substitute n = 3:

S₃ = S₃₋₂ · (S₃₋₁ − 1)

S₃ = S₁ · (S₂ − 1)

S₃ = 2 · (3 − 1)

S₃ = 4

Repeating this process, we get that the first nine terms of the sequence are:

2, 3, 4, 9, 32, 279, 8896, 2481705, 22077238784

2. "Compute the value of ∑(k=1 to 8) Sk, where Sk is the same sequence as in the previous question."

All we have to do here is add up the first 8 terms:

2 + 3 + 4 + 9 + 32 + 279 + 8896 + 2481705

= 2490930

3. "Is the sequence from question 1 arithmetic, geometric, or neither?  Explain how you reach your conclusion."

If the sequence were arithmetic, it would have a common difference.  But the difference between 3 and 4 is not the same difference between 4 and 9.

If the sequence were geometric, it would have a common ratio.  But the ratio between 2 and 3 is not the same ratio between 3 and 4.

So the series is neither arithmetic nor geometric.

4. "Find the sum of the first 200 terms of the arithmetic sequence that begins: 12, 18, 24..."

The sum of the first n terms of an arithmetic sequence is:

S = n (a₁ + aₙ) / 2

where a₁ is the first term and aₙ is the nth term.

The nth term of an arithmetic sequence is:

aₙ = a₁ + d (n − 1)

where d is the common difference.

Here, the first term is 12, so a₁ = 12.  The common difference is 18 − 12 = 6.  So the 200th term is:

a₂₀₀ = 12 + 6 (200 − 1)

a₂₀₀ = 1206

The sum of the first 200 terms is:

S = 200 (12 + 1206) / 2

S = 121800

You might be interested in
What would be the final elevation if a moth is flying at at 9 meters above the ground and changes by -4?
quester [9]
5 because this is equivalent to 9-4 which is 5 meters, this is because he is going up 9 and then goes down 4, do 9-4, which is 5
6 0
2 years ago
Find an equation of the tangent to the curve at the given point by both eliminating the parameter and without eliminating the pa
liubo4ka [24]
Im sorry i need points , i am really sorry
4 0
3 years ago
PLEASEEE HELLPPP!!!!!!!!
belka [17]

Answer:

4.25 i think

Step-by-step explanation:

sorry i    have not done these in a while it might be wrong

5 0
3 years ago
A deli offers up to 12 different toppings on their sub sandwiches how many different 4 topping sandwiches are possible
Rashid [163]
There are 3 because 12 divided by 4 is 3.
4 0
3 years ago
HELPPP PLSS <br><br><br><br> WILL GIVE BRAINLIST <br><br><br><br><br> MMM
Liula [17]

Answer:

29.5m

29.5m

29.5m

29.5m

Step-by-step explanation:

5m×5.9m

=29.5m

8 0
3 years ago
Other questions:
  • ______ are two angles that add up to 180° that share a common vertex.
    7·2 answers
  • There are 27 students in a class. 13 are
    8·1 answer
  • In describing the expression, which term would not be used? Will choose brainliest.
    15·1 answer
  • Find a8 when a1 = 40,000, r = 0.1
    5·2 answers
  • Finding values or<br> k(x) = x - 2<br> h(x) = x2 +1<br> (h + k)(2) =
    7·1 answer
  • On Sunday morning the temperature was 8°F. By Sunday evening the
    13·1 answer
  • Kiran's mother gets a restaurant bill for $25. She has a coupon for 15%. After the discount is applied, she adds 20% as a tip. W
    7·1 answer
  • Point X of triangle XYZ is located at (-5, -6). If triangle XYZ is translated 3 units
    12·1 answer
  • One winter's day the temperatures were recorded in five different cities in New York State. The table below shows the results of
    6·1 answer
  • 1) If there are 54 people in a class and the ratio of girls to total people is 2:5, how many
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!