Geometric Progression - C2

Hi i was set 20 questions for hwk on the whole of this chapter and there are 4 that i cant do - i would be very appreciative if you could help with the following for rep:

1) I invest £A in the bank at a rate of interest of 3.5% per annum. How long will it take before i double my money.

2) A ball is dropped from a height of 7m and continues to bounce. Subsequent heights to which it bounces follow a geometric sequence. Find out the total distance travelled until it hits the ground for the sixth time

Im using the general formula.. but cant get answer of 48.8234

3) Find the least value of n such that the sum 3 + 6 + 12 +24 to n terms would first exceed 1.5 million.

Did something like this in a previous question - used logs and i got it right however, cant get same answer in back of book

4) The first 3 terms of a geometric series are p(3q+1), p(2q+2) and p(2q-1) respectively, where p and q are non-zero constants.

a) use algebra to show that one possible value of q is 5 and to find the other possible value of q

b) For each possbile value of q, calculate the value of the common ratio - Should be able to do this if i have answer to a

Thank you all for your time and effort,

Regards, Asad

OP

Can any1 help?

asadtamimi

Hi i was set 20 questions for hwk on the whole of this chapter and there are 4 that i cant do - i would be very appreciative if you could help with the following for rep:

1) I invest £A in the bank at a rate of interest of 3.5% per annum. How long will it take before i double my money.

2) A ball is dropped from a height of 7m and continues to bounce. Subsequent heights to which it bounces follow a geometric sequence. Find out the total distance travelled until it hits the ground for the sixth time

Im using the general formula.. but cant get answer of 48.8234

3) Find the least value of n such that the sum 3 + 6 + 12 +24 to n terms would first exceed 1.5 million.

Did something like this in a previous question - used logs and i got it right however, cant get same answer in back of book

4) The first 3 terms of a geometric series are p(3q+1), p(2q+2) and p(2q-1) respectively, where p and q are non-zero constants.

a) use algebra to show that one possible value of q is 5 and to find the other possible value of q

b) For each possbile value of q, calculate the value of the common ratio - Should be able to do this if i have answer to a

Thank you all for your time and effort,

Regards, Asad

Q3)
sum= a(r^n-1)/(r-1)
1.5m =3(2^n -1)/1
1.5m=3.2^n-3
500,000=2^n -1
500,001=2^n
ln 500,001 = n.ln 2
n= (ln 500,001 )/(ln2) = 18.93 =>19

Reply 3

KAISER_MOLE

7

1) setting r=1.035 , find the first arⁿ > 2a

2) what is the coefficient of restitution of the ball? , it could very well bounce gerti high.

3) a=3 , r=2

=> sum = 3(2ⁿ-1)

=> first exceeds 1,500,000 when 2ⁿ exceeds 500,001

log₂500,001 = 18.93

=> n=19 is the lowest value of n to take to satisfy

4) (2q+2)/(3q+1) = (2q-1)/(2q+2) (=r)

=> (2q+2)² = (3q+1)(2q-1)

=> 4q² + 8q + 4 = 6q² - q - 1

=> 2q² - 9q - 5 = 0

=> (q-5)(2q+1) = 0

so q can either equal the stated 5, or it can equal -0.5

Reply 4

Aitch

2

asadtamimi

Hi i was set 20 questions for hwk on the whole of this chapter and there are 4 that i cant do - i would be very appreciative if you could help with the following for rep:

1) I invest £A in the bank at a rate of interest of 3.5% per annum. How long will it take before i double my money.

2) A ball is dropped from a height of 7m and continues to bounce. Subsequent heights to which it bounces follow a geometric sequence. Find out the total distance travelled until it hits the ground for the sixth time

Im using the general formula.. but cant get answer of 48.8234

3) Find the least value of n such that the sum 3 + 6 + 12 +24 to n terms would first exceed 1.5 million.

Did something like this in a previous question - used logs and i got it right however, cant get same answer in back of book

4) The first 3 terms of a geometric series are p(3q+1), p(2q+2) and p(2q-1) respectively, where p and q are non-zero constants.

a) use algebra to show that one possible value of q is 5 and to find the other possible value of q

b) For each possbile value of q, calculate the value of the common ratio - Should be able to do this if i have answer to a

Thank you all for your time and effort,

Regards, Asad

1)for ar^n=2a
1.035^n=2
ln 1.035.n=ln 2
n=ln 2/ln 1.035 = 20.1... so during 21st year

As Kaiser Mole says, we want more data for q2... say e or the height of the second bounce.

Reply 5

asadtamimi

OP

13

oh yea sorry bout that - a ball starts of at a height of 10m then after the first bounce rises to 6m then to 3.6 etc so the coefficient is 0.6 i make it.

By the way thanks a lot for your answers so far

Reply 6

Aitch

2

asadtamimi

oh yea sorry bout that - a ball starts of at a height of 10m then after the first bounce rises to 6m then to 3.6 etc so the coefficient is 0.6 i make it.

By the way thanks a lot for your answers so far

The original question had the start height as 7metres... Is it 7 or 10?

Reply 7

Aitch

2

Aitch

The original question had the start height as 7metres... Is it 7 or 10?

If it's 7
a=7 and r = 6/7

first work out one series:
Sum = a(1-r^n)/(1-r)
=7(1-(6/7)^6)/(1/7)=29.57

Then double this and subtract 7 because the ball goes up and down at each distance, except at the beginning

(29.57 x 2) - 7 = 52.14 This is not your book's answer, however!

If it's 10, the method is the same.

Reply 8

asadtamimi

OP

13

Im sorry , dont know whats wrong with me today - here is the question word for word :

A ball is dropped from a height of 10m. It bounces to a height of 7m and continues to bounce. Subsequent bounces follow a geometric sequence. Find out the total distance travelled until it hits the ground for the sixth time.

ignore the 6 and 3.6 data - thats from another question which i was able to do

Reply 9

Aitch

2

asadtamimi

Im sorry , dont know whats wrong with me today - here is the question word for word :

A ball is dropped from a height of 10m. It bounces to a height of 7m and continues to bounce. Subsequent bounces follow a geometric sequence. Find out the total distance travelled until it hits the ground for the sixth time.

ignore the 6 and 3.6 data - thats from another question which i was able to do

a=10 and r = 0.7

first work out one series:
Sum = a(1-r^n)/(1-r)
=10(1-(0.7)^6)/(0.3)=29.4117

Then double this and subtract 10 because the ball goes up and down at each distance, except at the beginning

(29.4117 x 2) - 10 = 48.8234 Eureka!

Reply 10

asadtamimi

OP

13

thanks a lot man - i repped u for it even tho its not worth much