Question

find the 10th term of the geometric progression 7 18 29?​

Answer 1

⇒ar³⁻¹ = 24  

⇒ar² = 24           (i)  

⇒ar⁶⁻¹ = 192  

⇒ar⁵ = 192         (ii)  

Now Divide (ii) by(i)  

⇒ar⁵/ar² = 192/24  

⇒r³ = 8  

⇒r =∛(8)  

⇒r=2    

Now put the value of r on (ii) eq  

⇒ar⁵ = 192  

⇒a(2)⁵ = 192  

⇒32a = 192

⇒a= 192/32  

⇒a= 6

Now we have to find a₁₀  

⇒a₁₀ = ar¹⁰⁻¹  

Where a = 6 and r = 2

⇒a₁₀ = 6×(2)⁹  

⇒a₁₀ = 512×6  

⇒a₁₀ = 3072

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