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
vfiekz [6]
3 years ago
15

For each explicitly-defined sequence below, write the first few terms. Then use the terms to write a recursive equation.

Mathematics
1 answer:
julia-pushkina [17]3 years ago
6 0

Answer:

Step-by-step explanation:

Problem A

t(1) = 2(1) + 5

t(2) = 2*2 + 5 = 9

t(3) = 2*3 + 5 = 11

t(4) = 2*4 + 5 = 13

So this is the explicit result. Now try it recursively.

t_3 = t_2 + 2

t_3 = 9 + 2

t_3 = 11          which is just what it should do.

t_n = t_(n - 1) + 2

Problem B

t(1) = 3 * 1/2

t(1) = 3/2

t(2) = 3*(1/2)^2

t(2) = 3 * 1/4

t(2) = 3/4

t(3) = 3*(1/2)^3

t(3) = 3 * 1/8

t(3) = 3/8

t(4) = 3 (1/2)^4

t(4) = 3 (1/16)

t(4) = 3/16

So in general

t_n = t_n-1 * 1/2

For example t(5)

t_5 = t_4 * 1/2

t_5 = 3 /16 * 1/2 = 3/32

You might be interested in
(03.01 LC)
vampirchik [111]

Answer:

√7 units, √98 units

Step-by-step explanation:

Pythagorean theorem

a^2+b^2=c^2. So 9+b^2=16. So b^2=7. So b=√7

a^2+b^2=c^2. SO 49+49=c^2. So 98=c^2. So c=√98.

4 0
3 years ago
Read 2 more answers
The pendulum swings at an arc of 30 cm and its successive swings reduced to 10% of the previous swings. What is the total distan
OleMash [197]

Answer:

S_g=  33.333cm

Step-by-step explanation:

From the question we are told that

Arc of 30 cm

10% reduction after each swing

Generally sum of geometric sequence is given by the equation

    S_g=\frac{a(1-r^n)}{1-r}

Mathematically solving for total distance traveled we have

    S_g=\frac{30(1-(0.10^5)}{1-(0.10)}

    S_g=\frac{30}{0.9}

Therefore the total distance traveled  by the pendulum after 5 swings

    S_g=  33.333cm

3 0
3 years ago
Y-2=4(x+3) what the slope intercept
Kryger [21]

Answer:

Slope intercept form: y = 4x + 14

Slope: 4

Y-intercept: 14

Step-by-step explanation:

y - 2 = 4(x + 3)

Use distributive property

y - 2 = 4x + 12

y - 2 + 2 = 4x + 12 + 2

y - 0 = 4x + 14

y = 4x + 14

3 0
2 years ago
Tom asked his Granny how old she was. Rather than giving him a straight answer, she replied: "I have 6 children, and there are 4
Ede4ka [16]

Answer: 58 years old

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Maxwell is taking out a loan for $8,750 for 2 years at an APR of 9.75%. What would be the finance charge to the nearest whole do
Sladkaya [172]

Answer:

Step-by-step explanation:

Using the formula for calculating simple interest

SI = principal × rate × time/100

Given

Principal = $8750

Rate = 9.75%

Time = 2years

Substitute

Interest = 8750×9.75×2/100

Interest = 87.59×19.5

Interest = 1,706.25

Hence the finance charge to the nearest whole dollar is $1706

8 0
3 years ago
Other questions:
  • One line passes through the points (2,1) and (5,7). Another line passes through points (-3,8) and (8,3). Are the lines parallel,
    9·2 answers
  • What is 2(x+6)=20 pls I need help
    5·2 answers
  • I rlly need the answer to this asap thanks
    10·1 answer
  • Please please please please answer now and please please explain thank you so much so so so much
    8·1 answer
  • Plants capturing light energy to from simple sugars using water and carbon dioxide is called
    7·1 answer
  • Suppose that the cost of a paving stone is $2.50, plus $0.15 for every 4 cubic inches of concrete.
    12·1 answer
  • What should be the value of x so that the three consecutive terms will be in GP 2x+2, 16 and 64x. Also find the sum of first 10
    7·1 answer
  • NEED HELP ASAP!!!! WILL MARK BRAINLIEST!!!!
    13·1 answer
  • HELP ASAP WILL GIVE BRAINLIEST!!!!
    6·1 answer
  • 9 and 1/9 subtracted by 1 and 4/5
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!