Arithmetic and Geometric Mean >< (1 Viewer)

[Inexorably Me]

Hey guys, my teacher gave me the formula for AP mean (b= [a+c] / 2) but i couldnt apply it to the Q: Find AP Mean of 5&51 (Ans: 287). I also dont know the formula for GP mean. Please help? and thank you

 

[AlexJB]

Well the mean would just be the sum of the series divided by the number of terms.

So for an AP, if we let a=first time, l=last term:
Sn = 1/2n(a + l)
Sn/n = 1/2(a+l)
= 1/2(5+51)
= 28 (assuming by 5&51, you mean 5 is first term, 51 is last term)

Same logic applies to a GP.
Sn = a(r^n - 1)/(r-1)
Sn/n = a(r^n - 1)/n(r - 1)

 

[Trebla]