Sequences & Series...help please? (1 Viewer)

[J-C-C]

Can someone please help me answer this question? ><

The second term of a geometric series is 2 and its limiting sum is 9. Find the values of first term a and common ratio r.


thanks

 

[Trebla]

Can someone please help me answer this question? ><

The second term of a geometric series is 2 and its limiting sum is 9. Find the values of first term a and common ratio r.


thanks

The geometric series takes the form:
a + ar + ar² + ..........
The second term = 2
=> ar = 2
Limiting sum = 9
=> a/(1 - r) = 9
a = 9(1 - r)
Sub into first equation:
9r(1 - r) = 2
9r - 9r² = 2
9r² - 9r + 2 = 0
(3r - 1)(3r - 2) = 0
r = 1/3 or r = 2/3
When r = 1/3, a = 6
When r = 2/3, a = 3

 

[J-C-C]

thank u SOOOOO much!
i really appreciate ur help x)