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In the given A.P, what will be the missing terms?

$7, x, y, z, 27$

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x=12, y=18, z=22

x=12, y=17, z=22

x=12, y=20, z=25

x=15, y=19, z=22

answer is B.

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Detailed Solution

Given,

A . P = 7, x, y, z, 27

.
The nth term of an arithmetic progression with ‘a’ as the first term and the common difference ‘d’ is

a n = a + n − 1 d

.
The first term will be

a 1 = 7

.
The last term is

a 5 = 27

.
The number of terms is

n = 5

The common difference will be,

⇒ 27 = 7 + 5 − 1 d ⇒ 27 − 7 = 4 d ⇒ 204 = d ⇒ d = 5

Therefore, the common difference will be

5

.
The second missing term x of the series,

⇒ a 2 = 7 + 2 − 1 5 ⇒ a 2 = 7 + 5 ⇒ a 2 = 12

The third missing term y of the series,

⇒ a 3 = 7 + 3 − 1 5 ⇒ a 3 = 7 + 10 ⇒ a 3 = 17

The fourth missing term z of the series,

⇒ a 4 = 7 + 4 − 1 5 ⇒ a 4 = 7 + 15 ⇒ a 4 = 22

Thus, the missing terms will be x=12, y=17, z=22.
Therefore the correct option is 2.

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