If three numbers are in GP,then the numbers obtained by adding the middle number to each of the three numbers are in ?
Please its very urgent help me guys with step by step explanation don't give irrelative answers i will report it
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Answer:
Let the numbers be a,b,c
∴b
2
=ac
Numbers obtained by adding middle number to each number are a+b,2b,b+c
Let us consider
a+b
1
+
c+b
1
=
ac+b
2
+bc+ac
a+c+2b
=
2b
2
+ab+bc
a+c+2b
=
(b)(a+c+2b)
a+c+2b
=
2b
1
∴a+b,2b,b+c are in HP
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