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Ii. For a G.P.Sum of first 3 terms is 125 and sum of next 3 terms is 27. Find the value of r.please answer mefollow me.. |
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Answer» Step-by-step EXPLANATION:Sum of first 3 terms = 125Sum of next three terms = 27The value of r➔ Let us assume the first term of the A.P as a➔ Hence, The second term = ar The third term = ar²➔ By given, Sum of first 3 terms = 125 a + ar + ar² = 125➔ Taking a as common, a (1 + r + r²) = 125 1 + r + r² = 125/a -------(1)➔ Now, Fourth term = ar³ Fifth term = ar⁴ Sixth term = ar⁵➔ Also by given, Sum of next 3 terms = 27 ar³ + ar⁴ + ar⁵ = 27➔ Taking ar³ as common, ar³ (1 + r + r²) = 27 1 + r + r² = 27/ar³ -------(2)➔ From EQUATIONS 1 and 2, LHS are EQUAL, hence RHS must also be equal. 125/a = 27/ar³➔ Cancelling a on both sides, 125 = 27/r³ 125 r³ = 27 r = 27/125 r = ∛ (27/125) r = 3/5➔ Hence the value of r is 3/5. |
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