Question

For a GP if S3=125, S6=152, find r​

Answer 1

Answer:

r = 3/5

Step-by-step explanation:

S3 = a(r^3 -1)/(r-1)

125= a(r^2 + 1 + r) ....(1)

Also, S6 = a(r^6 - 1)/(r-1)

152= a(r^3 +1)(r^3 - 1)/(r-1)

152 = a(r^3 + 1)(r^2 + 1 + r) ...(2)

(2)/(1) :

152/125 = r^3 + 1

r^3 = (152-125)/125

r = 3√(27/125)

= 3/5

Answer 2

Answer:

r=3/5

Step-by-step explanation:

S3=a(r3-1)/(r-1)

125=a(r2+1+r).........(1)

S6=a(r6-1)/(r-1)

152=a(r3+1)(r3-1)/(r-1)

152=a(r3+1)(r2+1+r).........(2)

Dividing equation 1 and 2

152/125=r3+1

r3=(152-125)/125

r=3Г27/125

r=3/5

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