Match each sequence to its appropriate recursively defined function

Mathematics

1 answer:

aniked [119]3 years ago

7 0

Answer:

f(1) = -24; f(n) = 4·f(n-1)
f(1) = 13; f(n) = f(n-1) + 26
f(1) = 28; f(n) = -4·f(n-1)

Step-by-step explanation:

Identify the first term of the sequence. First terms are -24, 13, 28. Find the matching f(1). There are two choices for each first term.

Then determine the relation of each term to the previous term. In two of the sequences, a factor of 4 is involved. For the sequence starting with -24, the adjacent terms have the same sign, so the factor is +4. For the sequence starting with 28, adjacent terms have alternating signs, so the factor is -4.

For the sequence starting with 13, the second term is 3 times the first, but it is also 26 added to the first. You have to look at the next term to see if the sequence is geometric with a ratio of 3, or arithmetic with a difference of 26. The latter is the case, so the recursive definition will involve addition, not multiplication.

The recursively defined functions are shown above in the order of the given sequences.

You might be interested in

Consider the problem $minimize$ $f(x)=x^4-1$. solve this problem using newton's method. start from $x_0=4$ and perform three ite

stellarik [79]

F(x)=x⁴-1
f'(x)=4x³
Newton’s Method: x[n+1]=x[n]-f(x[n])/f'(x[n]); x[n+1]=x[n]-(x[n]⁴-1)/4x[n]³
x₁=3.00390625
x₂=2.26215...
x₃=1.7182...

X'=X-(X⁴-1)/4X³=X-X/4+1/4X³ is a symbolic way of writing the recursive formula, where X' represents the next iteration.
When X'≈X, -X/4+1/4X³≈0; so X/4≈1/4X³; X≈1/X³, so X⁴≈1 and X⁴-1≈0. But this is f(x)≈0. Hence Newton’s Method converges to a solution.
The rate of change is x[n+1]-x[n]=-(x[n]⁴-1)/4x[n]³=x[n]/4-1/4x[n]³ or symbolically -X/4+1/4X³.
Note that the method converges to one solution. A different x₀ will possibly converge to the solution x=-1.

5 0

3 years ago

Find the measure of ZAOC. A 33° B. 38° C. 610 D. 71°

mart [117]

33+38 = 71
Answer D. 71

6 0

3 years ago

Read 2 more answers

Three girls bought a pizza for lunch. One girl ate 1/3 of the pizza another girl ate 1/4 of the pizza and the third ate the rest

Bad White [126]

One ate 1/3, Another ate = 1/4.

Total ate = 1/3 + 1/4 = (4 + 3) / 12 = 7/12

Fraction the third girl got = (The whole =1) minus 7/12

= 1 - 7/12 = (12 - 7) / 12 = 5/12

The third girl ate 5/12 of the pizza.

3 0

4 years ago

Determine the number of possible solutions for a triangle with B=37 degrees, a=32, b=27

vladimir1956 [14]

Answer:

Two possible solutions

Step-by-step explanation:

we know that

Applying the law of sines

$\frac{a}{sin(A)}=\frac{b}{Sin(B)}=\frac{c}{Sin(C)}$