Question

For a G.P sum of first 3 terms is 125 and sum of next 3 terms is 27 find the value of r.

Answer 1

Answer:

r = 3/5

Step-by-step explanation:

For a G.P sum of first 3 terms is 125 and sum of next 3 terms is 27 find the value of r.

Let say GP is

a , ar , ar² , ar³ , ar⁴ , ar⁵

sum of first 3 terms is 125

=> a + ar + ar² = 125

=> a(1 + r + r²) = 25

sum of next 3 terms is 27

=> ar³ + ar⁴ + ar⁵ = 27

=> ar³(1 + r + r²) = 27

=> r³a(1 + r + r²) = 27

=> r³ * 125 = 27

=> r³ = 27/125

=> r³ = (3/5)³

=> r = 3/5

Value of r = 3/5

Answer 2

Answer : (c) 3/5

Explanation:Sn=arn−1r−1inGP

Giventhat

S3S6=a(r3−1/r−1)a(r6−1/r−1)=125/152

Assumingr≠1

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

a(r3−1/r−1)a(r6−1/r−1)=125/152

r3−1r6−1=125/152

152r3−152=125r6−125

125r6−152r3−27=0

125r3(r3−1)−27(r3−1=0)

(125r3−27)(r3−1)=0

125r3=27orr3−1=0

r3=27/125r=1

r=3/5r≠1

r=3/5 answer