Question

A G.P consist of 2n terms. If the sum of the terms occupying the odd places is S(1) and that of the terms occupying the even places is S(2) , then find common ratio of the progression

Answer 1

I am stuck

Answer 2

We can see here the odd places and even places
then apply the sum of infinite terms in a G.P formula after that what should i do

Answer 3

what is S(1) ?

Answer 4

Oh there is no value given

Answer 5

i mean, what does it represent ?
or is it just some random constant like m,n ...

Answer 6

It represents sum of terms occupying the odd places. Yeah constant

Answer 7

s(1) is coming
a/1-r^3

Answer 8

they want common ratio in terms of S1 and S2 , right ??

a, ar, ar^2, ar^3 ,...

series odd : a, ar^2,ar^4 ... common ratio = r^2
S1 = a/(1-r^2 )

series even,
ar, ar^3 , ar^5....
S2 = ar /(1-r^2)

Answer 9

this turned out to be simple

Answer 10

just divide those

Answer 11

nopes,

r = S2/S1

Answer 12

S2 = ar /(1-r^2)
S1 = a/(1-r^2 )

a and 1-r^2 gets cancelled

Answer 13

yes s2/s1

Answer 14

sorry

Answer 15

np :)