If the numbers a, b , c ,d, e are in an A.P .
Find the value of a - 4b+6c - 4d +e.

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Solution

$\begin{matrix} W e h a v e a, b, c, d a n d e a r e i n A . P L e t a = x b = x + d c = x + 2 d d = x + 3 d e = x + 4 d N o w, a - 4 b - 4 c + 6 c - 4 d + e = x - 4 (x + d) + 6 (x + 2 d) - 4 (x + 3 d) + x + 4 d = (x - 4 x + 6 x - 4 x + x) + (- 4 d + 12 d - 12 d + 4 d) = 0 H e n c e, t h e v a l u e o f g i v e n A . P i s 0. \end{matrix}$

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