Thread: geometric series help asap!!! would be so appppreciated

please help, i do not understand this question at all:

a geometric series has first term a and common ratio r where r>1

the sum of the first n terms of the series is denoted by Sn.

given that S4= 10 x S2,

a) find the value of r

given that S3= 26,

b)find the value of a,

c) show that s6 = 728

The formula for a geometric series is Sn=a[(1-r^n)/(1-r)]
Given that:
S4=10S2
S3=26
r>1 (This is only important to avo1d division by zero)

Solution:
Since, S4=10S2 we have:
a[(1-r^4)/(1-r)]=10[(1-r^2)/(1-r)] multiply by (1-r):
a[(1-r^4)]=10[(1-r^2)] Factor (1-r^4):
a[(1-r^2)(1+r^2)]=10[(1-r^2)] divide by (1-r^2):
a(1+r^2)=10 THIS IS YOUR FIRST EQUATION.
Next:
Since S3=26 we have:
a[(1-r^3)/(1-r)]=26 Long divide 1-r^3 by 1-r to get:
a(1+r+r^2)=26 THIS IS YOUR SECOND EQUATION.
Next:
Divide the first equation by the second:
(1+r^2)/(1+r+r^2)=10/26 or 5/13. Cross Multiply:
13+13r^2=5+5r+5r^2 Collect Terms:
8r^2-5r+8=0
Which has no real solution thus your problem is impossible

Originally Posted by ThePerfectHacker

Since, S4=10S2 we have:
a[(1-r^4)/(1-r)]=10[(1-r^2)/(1-r)] multiply by (1-r):

implies:

or, cancelling a and (1-r):

or:

.

Which seems to have solution .

RonL

Next:
Since we have:

,

but from the first part we know that , so:

.

so .

Finally:

.

RonL

I new I did something wrong I forget the "a" term!