Question

If a b c are in ap then the value of (a+2b-c) (2b+c-a)(a+2b+c) is A.4a B.2a C.3 D. None of these

Answer 1

Answer:

answer for the given problem is given

Answer 2

ATQ:

a, b and c are in a AP.

To find:

(a + 2b - c) (2b + c - a) (a + 2b + c)

Solution:

First term of the AP → a

Second term of the AP → b

Third term of the AP → c

We know that b can be expressed as the sum of the preceeding term (a) and the succeeding term (c) divided by two since they all have a common difference.

$\sf \Longrightarrow b = \dfrac{a + c}{2}$

$\sf \Longrightarrow 2b =a + c \longmapsto \textcircled{\sf \scriptsize 1}$

Therefore;

⇒ (a + 2b - c) (2b + c - a) (a + 2b + c)

Substitute the value of 2b = a + c above.

⇒ (a + a + c - c) × (a + c + c - a) × (a + c + 2b)

⇒ (a + a) × (c + c) × (2b + 2b)

⇒ (2a) × (2c) × (4b)

⇒ (2) × (2) × (4) × (a) × (b) × (c)

⇒ 16abc

16abc isn't provided in the options, therefore, your answer will be (D) None of these.