Question

Give the ratio of sum of first three term of g.P to the sum of first six term is 125:152?

Answer 1

Ask Questions, Get Answers

 

Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class11  >>  Sequence and Series



Next similar question

Q)

 

In a GP, the ratio of the sum of first 3 terms to the sum of first 6 terms is 125/152. Find the common of the GP.

15/63/56/515/63/56/5



A)

 

Need homework help? Click here.

Answer : (c) 3/5

Explanation:Sn=arn−1r−1inGPExplanation:Sn=arn−1r−1inGP

GiventhatGiventhat

S3S6=a(r3−1/r−1)a(r6−1/r−1)=125/152S3S6=a(r3−1/r−1)a(r6−1/r−1)=125/152

Assumingr≠1Assumingr≠1

(asr−1isindenominatorξdenomitorcannotbe0,r−1≠0,r≠1)(asr−1isindenominatorξdenomitorcannotbe0,r−1≠0,r≠1)

a(r3−1/r−1)a(r6−1/r−1)=125/152a(r3−1/r−1)a(r6−1/r−1)=125/152

r3−1r6−1=125/152r3−1r6−1=125/152

152r3−152=125r6−125152r3−152=125r6−125

125r6−152r3−27=0125r6−152r3−27=0

125r3(r3−1)−27(r3−1=0)125r3(r3−1)−27(r3−1=0)

(125r3−27)(r3−1)=0(125r3−27)(r3−1)=0

125r3=27orr3−1=0125r3=27orr3−1=0

r3=27/125r=1r3=27/125r=1

r=3/5r≠1r=3/5r≠1

Answer=r=3/5iscommonratio.


HOPE U LIKE IT!!!! :)