Question

*Find the value of (a + 2b − c)(2b + c − a)(c + a − b), if a, b, c, are in an A.P.*

1️⃣ (abc)/2
2️⃣ abc
3️⃣ 2abc
4️⃣ 4abc​

Answer 1

Explanation.

→ a, b, c are in Ap.

→ Therefore,

→ First term = a

→ common difference = d = b - a = c - b

→ 2b = a + c → conditions of an Ap.

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

→ put the condition in this equation.

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

→ ( 2a ) ( 2c ) ( b)

→ 4abc

→ Therefore,

→ Option [ D ] is correct answer.

→ More information.

→ Nth term of an Ap.

→ An = a + ( n - 1 ) d

→ Sum of Nth term of an Ap.

→ Sn = n/2 [ 2a + ( n - 1 ) d ]