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
Alenkinab [10]
3 years ago
9

How would I write this as a geometric recursive and explicit formula? Algebra 2

Mathematics
1 answer:
Kisachek [45]3 years ago
5 0
Denote the sequence by a_n with n\ge1.

Recursively:

The first number is a_1=8, and each successive number is twice the previous one. So a_2=16, a_3=32, a_4=64, ... .

In other words,

a_2=2a_1
a_3=2a_2
a_4=2a_3

and so in general,

a_n=2a_{n-1}

Explicitly:

We can arrive at this formula by, in a way, working backwards. If a_n=2a_{n-1}, that means a_{n-1}=2a_{n-2}, and so a_n=2(2a_{n-2})=2^2a_{n-2}, and so on. We would end up with

a_n=2a_{n-1}=2^2a_{n-2}=2^3a_{n-3}=\cdots=2^{n-2}a_2=2^{n-1}a_1

(You'll notice a pattern here: the exponent of the 2 and the index of the earlier term in the sequence add up to n. For example, 2^1a_{n-1}\implies 1+(n-1)=n.)

or simply

a_n=2^{n-1}\cdot8

Then the 15th term is obtained immediately by evaluating this rule at n=15. We get

a_{15}=2^{15-1}\cdot8=2^{14}\cdot2^3=2^{17}=131,072
You might be interested in
What is the sum of an even number plus an odd number?\
Grace [21]

Answer:

both

Step-by-step explanation:

The sum of an even number of odd numbers is even, while the sum of an odd number of odd numbers is odd.

7 0
3 years ago
What is the value of st divided by (6r) if r =5 and t =45
SVEN [57.7K]
Write "st div. by 6r" as

  st
-------
   6r
                                                                                   45s        15s        3s
If r =5 and t = 45, but s is unknown, then we get    --------- = --------- = -------
                                                                                    6(r)        2(5)        2
8 0
3 years ago
-6x +3 3/4 + 14x - 3.25
Nataly_w [17]

Answer:

8x +5

Step-by-step explanation:

that's what I got.................

4 0
2 years ago
Read 2 more answers
What is the slope of the line passing through the points (1,57) and (2,27)?
alex41 [277]

Answer:

m = -30

m = slope

Step-by-step explanation:

(1,57) and (2,27)

(x1,y1) and (x2,y2)

y2 - y1.       27 - 57

----------  =.  ----------  =.  -30/1 = -30

x2-x1.           2 - 1

5 0
3 years ago
Read 2 more answers
The cost of painting a wall that is 5 meters wide and 212 meters tall is $50. How many square meters can be painted for $1?
tigry1 [53]

Answer:

21.2 square meters

Step-by-step explanation:

The area of a parallelogram is base • height.

So:

1. Calculate the area of what you can get for $50. 5 • 212 = 1060 square meters.

2. Now you divide the first price ($50) by the desired price ($1). This one is easy because 50 / 1 = 50, but I'm putting this here for future reference in case you need to solve a problem that has a desired price that's greater than $1.

3. Divide the answer to step one by the answer to step two to get the area you can have painted for $1. 1060 / 50 = 21.2 square meters.

3 0
2 years ago
Other questions:
  • What is the answer to this following equation (2•5)-56+102(4•215)
    9·1 answer
  • Income Vincent earns $15 per hour during the week and $18 per hour for overtime
    10·1 answer
  • If j, k, and n are consecutive integers such that 0 < j < k < n and the units (ones) digits of the product jn is 9, wha
    11·1 answer
  • Which statement best describes the value of V8? I’m so confused:((
    8·2 answers
  • A) Which of triangle A, B, C and D is congruent to triangle E.? B) Which other two triangles (from A, B, C and D) are congruent
    14·1 answer
  • You spin the spinner shown below once. The spinner has 4 equal sectors colored pink, purple, blue and green. What is p ( not pur
    15·1 answer
  • Write a function using function notation to describe each situation. Find a reasonable domain and range for each function.
    13·1 answer
  • Complete the table.
    6·1 answer
  • Chris had $56 to
    11·1 answer
  • There are 5 Germans and 5 Italians in an English class. If a group of 3 is going to be created, what is the probability that eve
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!