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Question

If a,b,c are in A.P. and a,b,d are in G.P. then  a,a-b,d-c are in


Solution

a,b ,c are in ap

so 2b =a +c

and a,b ,d are in GP

b2= ad

now a, a-b , d-c

a-b / a = d-c / a-b

(a-b)2= a(d-c)

a2+b2-2ab = ad - ac

a2+ ad - a(a+c) = ad - ac

a2- a2- ac = -ac

ac =ac TRUE......

hence a, a-d , d-c are in GP


Mathematics

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