First slide

Arithmetic progression

Question

In a set of four numbers the first three are in G.P. and the last three are in A.P. with a common difference 6. If the first number is same as the fourth, the four numbers are

Moderate

A

3, 9, 15, 21
B

1, 7, 13, 19
C

8, – 4, 2, 8
D

None of these

Solution

Let the last three numbers in A.P. be b, b + 6, b + 12
and the first number be a.
Hence the four numbers are a, b, b + 6, b + 12
Given, a=b+12 (1)
and a, b, b + 6 are in G.P. i.e., b2 = a (b + 6)
or b² = (b + 12) (b + 6) ( $∴$ a = b + 12)
or 18b = – 72 \ b = –4,
From Eq. (1),
a = – 4 + 12 = 8.
Hence, the four numbers are 8, –4, 2 and 8.

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