Q. 7

# The product of three numbers in G.P. is 216. If 2, 8, 6 be added to them, the results are in A.P. Find the numbers.

Let the three numbers be .

According to the question

…(1)

a3 = 216

a = 6

The above sequence is in AP.

We know in AP.

2b = a + c

Substituting a = 6 in above equation we get,

28r = 6 + 6r2 + 8r

6r2 – 20r + 6 = 0

6r2 – 18r – 2r – 6 = 0

6r(r – 3) – 2(r – 3) = 0

(6r – 2) (r – 3) = 0

r = 3 or r = 1/3 .

Now the equation will be

2,6,18 or 18,6,2

The three numbers are 2,6,18.

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