Question

If a, b, c, d, e are in A.P., then the value of a - 4b + 6c - 4d + e is ______.

Options

• 0

• 1

• -1

• 2

Answer 1

If a, b, c, d, e are in A.P., then the value of a - 4b + 6c - 4d + e is 0.

Explanation:-

Let common difference of A.P. be x

∴ b = a + x, c = a + 2x, d = a + 3x and e = a + 4x

Given equation a - 4b + 6c - 4d + e

= a - 4(a + x) + 6(a + 2x) - 4(a + 3x) + (a + 4x)

= a - 4a - 4x + 6a + 12x - 4a - 12x + a + 4x

= 8a - 8a + 16x - 16x

= 0