in a GP which begins with first the sum of three terms is 13 find the common ratio
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Answer:
r=3,1/3
Step-by-step explanation:
The sum of the first three terms of a GP is 13:
a+ar+ar2=13(1)
The sum of the squares of these terms is 91:
a2+a2r2+a2r4=91
(a2+2a2r2+a2r4)−a2r2=91
(a+ar2)2−(ar)2=91
(a+ar2−ar)(a+ar2+ar)=91
(a−ar+ar2)(13)=91
a−ar+ar2=7(2)
(1)−(2)
2ar=6
ar=3
(1)+(2)
2a+2ar2=20
ar+(ar)r2=10r
3+3r2=10r
3r2−10r+3=0
(r−3)(3r−1)=0
r=3,1/3
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