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A G.P. contains 2n terms . If the sum of terms occupying odd places is S1 and that of occupying even places is S2 ,then find common ratios

A G.P. contains 2n terms . If the sum of terms occupying odd places is S1 and that of occupying even places is S2 ,then find common ratios

Grade:11

2 Answers

Arun
25763 Points
3 years ago
In S1 and S2 formula,We see thatVariables are n, a, rNow n will be same for both, r will be same for both but a is different.As for S1, if first term = aThen for S2, it will be = a*rHence in formula of sumIf we compare thenS1/S2 = a/arHence r = S2/S1
Sabreen anjum
13 Points
2 years ago
N=2n
Sum of first odd terms =S1
a1,a3,a5,a7,...........a2n=S1
a1(rñ-1)/r-1=S1
Sum of first even terms=S2
a2,a4,a6,a8,...........,a2n=S2
a2(rñ-1)/r-1=S2
By taking ratios of both S ,
S1/S2=a1(rñ-1)/r-1\a2(rñ-1)/r-1
All the quantities are like r ,n equal except a1 and a2 mean the first terms 
a1=a and a2=ar because they are in g.p.
S1/S2=a1/a2
S1/S2=a/ar
S1/S2=1/r
r= S2/S1

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