The sum of first 3 term of GP : the sum of 6 terms of GP as 125:152 find the common ratio
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Sum of nth term in GP (Sn)= a(rⁿ ➖1)/(r ➖1)
so
S3➗S6 = 125➗152
{a(r³ ➖ 1)/(r ➖1)}/{a(r^6 ➖1)/(r ➖1)} = 125➗152
(r³ ➖1)/(r³ ➖1)(r³➕1) = 125➗152
1/(r³ ➕ 1) = 125➗152
152 = 125r³ ➕ 125
27 =125r³
27➗125 = r³
(3➗5)³ = r³
r = 3➗5
thank you
Sum of nth term in GP (Sn)= a(rⁿ ➖1)/(r ➖1)
so
S3➗S6 = 125➗152
{a(r³ ➖ 1)/(r ➖1)}/{a(r^6 ➖1)/(r ➖1)} = 125➗152
(r³ ➖1)/(r³ ➖1)(r³➕1) = 125➗152
1/(r³ ➕ 1) = 125➗152
152 = 125r³ ➕ 125
27 =125r³
27➗125 = r³
(3➗5)³ = r³
r = 3➗5
thank you
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