please help me be fast. .
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let 》
》m is the Arithmetic mean of a and b
》So, m = (a+ b)/2 ⇒2m = a+ b ----(1)
》Again,a , G₁ , G₂ , G₃ and b are in GP .
》So,
》we can assume common ratio r
》G₁ = ar , G₂ = ar² , G₃ = ar³ and b = ar⁴
》b/a = r⁴ -------(2)
》Now,
》G₁⁴ + 2G₂⁴ + G₃⁴ = (ar)⁴ + 2(ar²)⁴ + (ar³)⁴ =
》= a⁴r⁴[1 +2 r⁴ + r⁸ ]
》= a⁴ × b/a × [1 + r⁴]² [ from equation (2) , r⁴= b/a]
》= a³n × [1 + b/a]² = a³n/a²[a + b]² = ba (2m)² 》
》 ( = 4abm²)ans
your answer is option (a) is right
let 》
》m is the Arithmetic mean of a and b
》So, m = (a+ b)/2 ⇒2m = a+ b ----(1)
》Again,a , G₁ , G₂ , G₃ and b are in GP .
》So,
》we can assume common ratio r
》G₁ = ar , G₂ = ar² , G₃ = ar³ and b = ar⁴
》b/a = r⁴ -------(2)
》Now,
》G₁⁴ + 2G₂⁴ + G₃⁴ = (ar)⁴ + 2(ar²)⁴ + (ar³)⁴ =
》= a⁴r⁴[1 +2 r⁴ + r⁸ ]
》= a⁴ × b/a × [1 + r⁴]² [ from equation (2) , r⁴= b/a]
》= a³n × [1 + b/a]² = a³n/a²[a + b]² = ba (2m)² 》
》 ( = 4abm²)ans
your answer is option (a) is right
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