if-a-b-c-d-e-are-in-AP-find-the-value-of-a-4b-6c-4d-e-please-help-i-do-not-know-where-to-begin-

Question Number 99575 by MWSuSon last updated on 21/Jun/20

if a, b, c, d, e are in AP . find the value

of a - 4 b + 6 c - 4 d + e .

please help, i do not know where to

begin .

Answered by mathmax by abdo last updated on 21/Jun/20

take a try first \dots

Commented by MWSuSon last updated on 21/Jun/20

okay sir, although I've tried, but your comment gives me a little assurance that it looks easier than I think.

Commented by mathmax by abdo last updated on 21/Jun/20

perhaps \dots

Commented by MWSuSon last updated on 22/Jun/20

a, b, c, d, e

b = a + k

c = a + 2 k

d = a + 3 k

e = a + 4 k

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

(a + e) + 6 c - 4 (b + d)

= (2 a + 4 k) + 6 a + 12 k - 4 (2 a + 4 k)

= 0 .

Thank you sir, you were right, i did

not give it a try .

Answered by mathmax by abdo last updated on 22/Jun/20

b = a + r, c = a + 2 r, d = a + 3 r and e = a + 4 r \Rightarrow

a - 4 b + 6 c - 4 d + e = a - 4 a - 4 r + 6 a + 12 r - 4 a - 12 r + a + 4 r

= 0