Given the formula for an arithmetic sequence f(9) = f(8) + 5 written using a recursive formula, write the sequence using an arithmetic formula. f(9) = f(1) + 5 f(9) = f(1) + 30 f(9) = f(1) + 35 f(9) = f(1) + 40

2 answers
Question:

Given the formula for an arithmetic sequence f(9) = f(8) + 5 written using a recursive formula, write the sequence using an arithmetic formula.
f(9) = f(1) + 5
f(9) = f(1) + 30
f(9) = f(1) + 35
f(9) = f(1) + 40

Answers

Answer:f(9)=f(1)+40Step-by-step explanation:We are given term=previous term+5 by the equation f(9)=f(8)+5 and that the sequence is arithmetic.This tells the slope of the line is 5. (We know it is linear because it is arithmetic).So we want to find the slope of the line going through (1,f(1)) and (9,f(9)).[tex]\frac{f(9)-f(1)}{9-1}=5[/tex][tex]f(9)-f(1)=5(9-1)[/tex][tex]f(9)-f(1)=5(8)[/tex][tex]f(9)-f(1)=40[/tex]

Answer:Option D.Step-by-step explanation:The recursive formula for an arithmetic sequence[tex]a_n=a_{n-1}+d[/tex]        .... (1)where, nis the number of term and d is the common difference.Given the recursive formula for an arithmetic sequence[tex]f(9)=f(8)+5[/tex]          .... (2)From (1) and (2) we get[tex]n=9,d=5[/tex]The explicit formula for an arithmetic sequence is[tex]a_n=a_1+(n-1)d[/tex]where, a1 is first term and d is common difference.Substitute n=9 and d=5 in the above formula.[tex]a_9=a_1+(9-1)(5)[/tex][tex]a_9=a_1+40[/tex]It can be written as[tex]f(9)=f(1)+40[/tex]Therefore, the correct option is D.

Similar Solved Questions

2 answers

What precent of 14 is 4.34?

What precent of 14 is 4.34?...
1 answer

Explain how changes in weather are caused by the interaction of air massas

Explain how changes in weather are caused by the interaction of air massas...
2 answers

Where was Hansel headed after escaping the ominous underworld?

Where was Hansel headed after escaping the ominous underworld?...
2 answers

1+1+1+1+1+1+1+1 / 5x10-2+60=?

1+1+1+1+1+1+1+1 / 5x10-2+60=?...
2 answers

There are 220 seniors at a certain school. Among all seniors, 45 took calculus, 55 took physics, and 10 took both. How many seniors took neither calculus nor physics? Please explain.

There are 220 seniors at a certain school. Among all seniors, 45 took calculus, 55 took physics, and 10 took both. How many seniors took neither calculus nor physics? Please explain....
1 answer

How many electrons are needed to equal the mass of a proton?

How many electrons are needed to equal the mass of a proton?...
1 answer

How does the automated system improve the effciency andvtimeliness of financial statements

how does the automated system improve the effciency andvtimeliness of financial statements...
1 answer

Japan invaded China in 1937. Why?

Japan invaded China in 1937. Why?...
2 answers

Find the value of: 0.0279 divided by 0.00009

Find the value of: 0.0279 divided by 0.00009...
1 answer

HELP DUE IN 15 MINS! In ΔABC, AB = 6 in, BC = 11 in, AC = 9 in. In ΔXYZ, XZ = 38.5 in, XY = 31.5 in, and YZ = 21 in.1. . Are the two triangles similar?Answer choices for number 1Yes, the sides are all proportional or No, the sides are not proportional.??2. What is the Scale Factor=??

HELP DUE IN 15 MINS! In ΔABC, AB = 6 in, BC = 11 in, AC = 9 in. In ΔXYZ, XZ = 38.5 in, XY = 31.5 in, and YZ = 21 in.1. . Are the two triangles similar?Answer choices for number 1Yes, the sides are all proportional or No, the sides are not proportional.??2. What is the Scale Factor=??...
1 answer

How many grams of Zn are in 0.356 mole of Zn?

How many grams of Zn are in 0.356 mole of Zn?...
1 answer

A sample of carbon monoxide gas occupies 150.0mL at 25.0 degrees Celsius. It is then cooled at a constant pressure until it occupies 100.0mL. What is the new temperature in degrees Celsius?

a sample of carbon monoxide gas occupies 150.0mL at 25.0 degrees Celsius. It is then cooled at a constant pressure until it occupies 100.0mL. What is the new temperature in degrees Celsius?...
1 answer

Check my answer?? What does the text describe? Attainment of lebensraum for the Aryan race Violation of the Munich Agreement Annexation of Austria Blitzkrieg into Poland A. actions take by Germany in response to aggressive acts by France B. responses by the League of nations for German aggression C. actions taken by Germany that lead to WWII (THIS ONE??) D. examples of appeasement by France and Great Britain

Check my answer?? What does the text describe? Attainment of lebensraum for the Aryan race Violation of the Munich Agreement Annexation of Austria Blitzkrieg into Poland A. actions take by Germany in response to aggressive acts by France B. responses by the League of nations for German aggression C....
2 answers

How many presidents were democrat

how many presidents were democrat...
1 answer

Can someone please help mee finish this?

Can someone please help mee finish this?...
2 answers

Super mario bros or mario 64

super mario bros or mario 64...
1 answer

Which answer here is the definition for this word or phrase?"sacred writings"scripturevariantdiction​

Which answer here is the definition for this word or phrase?"sacred writings"scripturevariantdiction​...
2 answers

Joyce lost 26 lbs on her diet. During vacation she gained 4 lbs. How much was her overall loss?

Joyce lost 26 lbs on her diet. During vacation she gained 4 lbs. How much was her overall loss?...
1 answer

A ball is thrown downward from the top of a building with an initial speed of 25m/s. it strikes the ground after 2.0s. how high is the building?

A ball is thrown downward from the top of a building with an initial speed of 25m/s. it strikes the ground after 2.0s. how high is the building?...

-- 0.049101--