In a gp the ratio of the sum of the first 3 terms is to that of first six terms is 125:152. Find the common ratio
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23
Answer:
Sum of nth term in GP (Sn)= a(rⁿ -1)/(r -1)
A/C to question,
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
hence, common ratio = 3/5
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Answered by
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Sum of nth term in GP (Sn)= a(rⁿ -1)/(r -1)
A/C to question,
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
hence, common ratio = 3/5
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