Question

If the numbers a b c d e form an ap then find the value of a-4b+6c-4d+e

Answer 1

let the terms be like,
a = p - 2d
b = p - d
c = p
d = p + d
e = p + 2d,
where, (p -2d) is the first term and +d is the common difference.
Then,
a-4b+6c-4d+e = (p-2d) - 4(p-d) + 6(p) - 4(p+d) + (p+2d)
= 8p - 4p + 4d - 4p - 4d
= 8p - 8p + 4d - 4d
So,
a-4b+6c-4d+e = 0

Hope you got help from my answer.

Answer 2

Answer:

let the terms be like,

a = p - 2d

b = p - d

c = p

d = p + d

e = p + 2d,

where, (p -2d) is the first term and +d is the common difference.

Then,

a-4b+6c-4d+e = (p-2d) - 4(p-d) + 6(p) - 4(p+d) + (p+2d)

= 8p - 4p + 4d - 4p - 4d

= 8p - 8p + 4d - 4d

So,

a-4b+6c-4d+e = 0