Quantitative Aptitude :: progressions - Discussion

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Explanation:
p=(a+b)/2; q=(b+c)/2
=> 1/p+1/q = 2*((1/(a+b))+(1/(b+c))
=> 2*(a+2b+c)/(a+b)(b+c)
=> 2*(a+2ar+a(r^2))/(a+ar)(ar+a(r^2)) because b=ar; c= a(r^2).
where r = common ratio.

On Solving, we get
=> 1/p + 1/q = 2/ar = 2/b.