If the numbers a, 9, b, 25 form an AP, find a and b from the following options.

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2, -16

1, 17

2, 16

-1, 17

answer is A.

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Detailed Solution

It is given that a, 9, b, 25 are in AP.
From the given information,

a 1 = a a 2 = 9 a 3 = b a 4 = 25

The consecutive terms have the same common difference.

a 2 − a 1 = a 3 − a 2 = a 4 − a 3 9 − a = b − 9 = 25 − b

Assume that,

9 − a = b − 9

a + b = 9 + 9

a + b = 18

……(1)
Now assume,

b − 9 = 25 − b

2 b = 25 + 9

2 b = 34

b = 17

The value of b is 17.
Substitute b = 17 in equation (1) to get the value of a,

a + 17 = 18 a = 1

The values of a and b are 1 and 17 respectively.
Hence, the correct option is 1.

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