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The product of 10th‚12th‚14th‚and 16th terms of G.P is 1296. find the 13th term. |
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Answer» Answer: 6 Step-by-step explanation: Given-----> Product of 10th , 12TH , 14th and 16th terms of GP is 1296 . To find-----> Find the 13th TERM Solution-----> Let first term and COMMON ratio of GIVEN GP be a and r . We know that, formula of nth term of GP is aₙ = a rⁿ⁻¹ => a₁₀ = a r¹⁰ ⁻¹ => a₁₀ = a r⁹ a₁₂ = a r¹²⁻¹ = ar¹¹ a₁₄ = a r¹⁴⁻¹ = a r¹³ a₁₆ = a r¹⁶⁻¹ = a r¹⁵ Now , ATQ, a₁₀ × a₁₂ × a₁₄ × a₁₆ = 1296 => a r⁹ × a r¹¹ × a r¹³ × a r¹⁵ = 1296 => a⁴ r⁹⁺ ¹¹ ⁺¹³ ⁺ ¹⁵ = 1296 => a⁴ r⁴⁸ = 1296 => ( a )⁴ ( r¹² )⁴ = 6 × 6 × 6 × 6 => ( a r¹² )⁴ = 6⁴ => a r¹² = 6 => a r¹³⁻¹ = 6 => a₁₃ = 6 |
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