Question

In a set of four numbers the first three are in G.P. and the last three in A.P.
with a common difference 6. If the first number is same as the fourth, the four
numbers are
(a) 3,9, 15, 21
(b) 1,7, 13, 19
(C) 8,- 4,2, 8
(d) None of these
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Answer 1

Answer:

Option c is correct.

Step-by-step explanation:

Last three of the four numbers are in A.P. and hence they may be chosen as a−d,a,a+d

Also the first number is same as the last one i.e. a+d.

Therefore the four numbers are a+d,a−d,a,a+d. The first three of the above four are in G.P.

∴(a−d)

2

=a(a+d). But d=6 given

∴(a−6)

2

=a(a+6)

or a

2

−12a+36=a

2

+6a

or 18a=36 ∴a=2.

Putting for a and d the four numbers are 8,−4,2,8, which satisfy the given conditions.