Question

If the numbers a, b, c, d and e from an A.P then find the value of a - 4b +6c -4 d +e

Answer 1

$a,b,c,d$ and $e$ are in $AP$

let $a=X$

$b=X+d$

$c=X+2d$

$d=X+3d$

$e=X+4d$

put the given value$,$

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

$X-4(X+d)+6(X+2d)-4(X+3d)+X+4d$

$=(X-4X+6X-4X+X)$ $+$ $(-4d+12d-12d+4d)$

=0+0=0

So$,$ the value of $a-4b+6c-4d+e=0$