Sequences (1 Viewer)

[davidbarnes]

How do you know whether a sequence is geometric or arithmetic?

 

[ianc]

an arithmetic series is simply where you add/subtract a common term

a geometric series is where you are multiplying/dividing by a common term - so as a result the series will increase/decrease much faster than an arithmetic series.

hope this helps!

 

[kokodamonkey]

if your given 3terms and if you CANT tell whether its an ap or gp.. lets say the terms are a,b,c
if it is an arithmetic one, then: c-b = b-a
if its a g.p then: c/b = b/a

hope that helps..

 

[Forbidden.]

if your given 3terms and if you CANT tell whether its an ap or gp.. lets say the terms are a,b,c
if it is an arithmetic one, then: c-b = b-a
if its a g.p then: c/b = b/a

hope that helps..

Question answered.

 

[kokodamonkey]

yeah im so cool

 

[Forbidden.]

yeah im so cool

The limiting sum of a geometric series is 5 and the second term is 6/5. Find the first term and the common ratio of the series.

 

[Robert1961]

Question

Given S = 5 & t2 = 6/5 find a & r

Answer

S = 5 = a / (1 – r) provided -1 < r < 1 & t2 = a.r = 6/5

Solve simultaneously

5 – 5r = a (#) & a = 6 / (5r)

5 – 5r = 6 / (5r) (both = a)

25r – 25r^2 = 6

0 = 25r^2 - 25r + 6

use quadratic formula to show that

r = 3/5 or 2/5 ( -1 < r < 1 both OK)

substitute into (#)

a = 5 – 3 or a = 5 – 2

a = 2 or a = 3

Final Solutions
(a,r) = (2 , 3/5) or (3 , 2/5)

Check Soultions
For both pairs S = 5 & t2 = 6/5. Therefore both solutions are correct.

 

[Forbidden.]

Question

Given S = 5 & t2 = 6/5 find a & r

Answer

S = 5 = a / (1 – r) provided -1 < r < 1 & t2 = a.r = 6/5

Solve simultaneously

5 – 5r = a (#) & a = 6 / (5r)

5 – 5r = 6 / (5r) (both = a)

25r – 25r^2 = 6

0 = 25r^2 - 25r + 6

use quadratic formula to show that

r = 3/5 or 2/5 ( -1 < r < 1 both OK)

substitute into (#)

a = 5 – 3 or a = 5 – 2

a = 2 or a = 3

Final Solutions
(a,r) = (2 , 3/5) or (3 , 2/5)

Check Soultions
For both pairs S = 5 & t2 = 6/5. Therefore both solutions are correct.

That was for kokodamonkey to solve, but nonetheless you got it correct ....

 

[Robert1961]

Sorry I did not realise your intentions.