Question

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

Answer 1

a, b, c, d, e are in A.P.
a = a
b = a + d
c = a + 2d
d = a + 3d
e = a + 4d
Substituting the values of b, c, d & e in
a - 4b + 6c - 4d + e
$= a - 4(a + d) + 6(a + 2d) - 4(a + 3d) + (a + 4d) \\ = a - 4a - 4d + 6a + 12d - 4a - 12d + a + 4d \\ = (a + a + 6a - 4a - 4a) + (12d - 12d + 4d - 4d) \\ = 8a - 8a + 0 \\ = 0$
Hence, the value of equation is 0.

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