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]
2 years ago
9

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

Mathematics
1 answer:
Kisachek [45]2 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
Round 1149 to the nearest thousand.
zysi [14]
1150, i’m pretty sure that’s it!
4 0
3 years ago
The difference between the squares of two consecutive numbers is 23. what are the two numbers?
Ksju [112]

(x+1)^2-x^2=23

x^2+2x+1-x^2=23

2x+1=23

2x=22

x=11

11^2 = 121

x+1 =12

12^2=144

144-121 = 23

4 0
3 years ago
How do I solve this?
Serhud [2]

Answer:

44.94

Step-by-step explanation:

Use trigonometric ratios to find the unknown side.

Since you are given the adjacent side and the opposite side is in question, use the tangent ratio.

tan(x) = opposite/adjacent

Replace the variables with given values.

tan(59) = x/27

Isolate the variable.

27tan(59) = x

Use a calculator to evaluate the answer.

x = 27tan(59) ≈ 44.94

Please mark as Brainliest! :)

8 0
3 years ago
point (4,4),(4,0), and (0,0) are the vertices of the triangle the enclosed whole squares and half squares on the grid. determine
Advocard [28]

Answer:

8

Step-by-step explanation:

finding the area is h x l x 1/2. The h is 4 and the l is also 4. That multiplied is 16. Multiply that by 1/2 and you get 8

6 0
2 years ago
Write 235 using powers of 10
vaieri [72.5K]

Answer:

(10^2)*2, 10*3, 10/2

Step-by-step explanation:

Thats my best guess to your very vague question

8 0
2 years ago
Other questions:
  • Help me please!!!!
    5·1 answer
  • Pleas help me with this problem. Urgent. Will mark BRAINLIEST.
    7·1 answer
  • What is 3 divided 76
    8·2 answers
  • Suppose this relation forms a function: {(3,-5), (-2,9), (0,4), (x,7)}. What values are not possible for the value of x?
    5·1 answer
  • What is the elapse time for start time. 3:48 pm to end time : 8:11 pm?
    7·1 answer
  • Simplify this expression<br><br> (3 + i) - (2- 2i)
    5·2 answers
  • Which equation can be used to solve for the unknown number? Seven less than a number is thirteen.
    14·2 answers
  • Surface area of a cylinder radius is 1 3/16 and the height is 4 3/4
    10·1 answer
  • What is the solution?
    6·2 answers
  • Help on a time limit!
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!