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Choose whether the given statement is true or false.

The sum of three numbers in G.P. is 14. If the first two terms are each increased by 1 and the third term decreased by 1, the resulting numbers are in A.P. Then the largest of those numbers is 4 and the smallest of those numbers is 1 .

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True

False

answer is B.

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Detailed Solution

Let the numbers be a, ar, a

r^{2}

then, Sum = a(1+r+

r^{2}

) = 14......(1) Also
a+1, ar+1, 4a

r^{2}

−1 are in A.P

\Rightarrow

r^{2}

−2r+1) = 2…..(2)
Divide (1) and (2) and simplifying
2

r^{2}

−5r+2 = 0
Or, r =2,

\frac{1}{2}

and hence a = 2,8
Numbers are 2,4,8 or 8,4,2
The required difference of = 6
Hence, the smallest number is 2 and the largest number is 8.
Hence the given statement is false.

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