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Question

# There are four numbers such that first three of them form an Arithmetic Progression and the last three form a Geometric Progression. The sum of the first and the third is 2 and that of second and fourth is 26. What is the sum of first and fourth number?

A
851325
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B
257385
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C
83
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D
none of these
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Solution

## The correct option is D none of theseLet a, b, c, d be four numbers such that a, b, c, are in A.P. and b, c, d are in G.P ∴a+c=2b...(1)andbd=c2...(2)Alsoa+c=2...(3)andb+d=26...(4)⇒b=1 from (4), d = 25 ∴ from (2) c = ± 5 when c = 5, then a = - 3 when c = -5, then a = 7 Hence the four numbers are - 3, 1, 5, 25 or 7, 1, -5, 25

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