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3 years ago

Write a recursive formula for each sequence given or described below.

Mathematics

1 answer:

lapo4ka [179]3 years ago

3 0

Answer:

Recursive form of sequence is given by f(n) = f(n-1) - 3

Step-by-step explanation:

The explicit form of sequence is given as

f(n) = −3n + 2

So nth term is given by

f(n) = −3n + 2

(n-1)th term is given by

f(n-1) = −3(n-1) + 2

We have

f(n) - f(n-1) = −3n + 2 - (−3(n-1) + 2)

f(n) - f(n-1) = −3n + 2 +3(n-1) - 2

f(n) - f(n-1) = −3n + 2 +3n -3 - 2

f(n) - f(n-1) = -3

f(n) = f(n-1) - 3

Recursive form of sequence is given by f(n) = f(n-1) - 3

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Wewaii [24]

Answer:

3(10 + 4) = 34 + 6 = 40

Step-by-step explanation:

Barbara has 30 school supplies plus an extra 4. Lisa on the other hand has 6. In total they have 40.

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3 years ago

Find the solution of the given initial value problem in explicit form. y' = (1 – 11x)y?, y(0) = -1 Enclose numerators and denomi

Tanya [424]

Answer:

$y(x)=-e^{x-(\frac{11*x^{2} }{2}) }$

Step-by-step explanation:

This is a separable equation. First divide both sides by y:

$\frac{dy(x)}{\frac{dx}{y(x)} } =-11x+1\\\frac{dy}{y}=(-11x+1)dx$

Integrate both sides:

$\int\ \frac{dy}{y} \ =\int\ (-11x+1) \, dx$

$log(y)=-(\frac{11*x}{2} )+x+ c_1$

Solve for y taking exp to both sides:

$y(x)=c_1*e^{x-(\frac{11*x^{2} }{2}) }$

Where $c_1$ is an arbitrary constant

Evaluating the initial condition:

$y(0)=c_1*e^{0-(\frac{11*0^{2} }{2}) } =-1$

$c_1*e^{0} =-1\\c_1*1=-1\\c_1=-1$

Finally, replacing $c_1$ in the differential equation solution:

$y(x)=-e^{x-(\frac{11*x^{2} }{2}) }$

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3 years ago

Carlt mowed 2 more lawns than rocco week for 5 weeks. Carlt mowed a total of 18 lawns. How many lawns did Rocco mow each week?

denis-greek [22]

Answer: 1.6 lawns a week

Step-by-step explanation:

Carlt mowed 2 more lawns than Rocco every week for 5 weeks.

This means that the number of lawns he mowed more than Rocco is:

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If Carlt mowed 18 lawns in those 5 weeks then Rocco mowed:

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= 8 lawns

Lawns mowed per week by Rocco:

= 8/5

= 1.6 lawns a week

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3 years ago

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Law Incorporation [45]

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aalyn [17]

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3 years ago