Question

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

Answer 1

Given $a,b,c,d,e$ are in $A.P$

Let $E=[a+e]-4[b+d]+6c$
Now
as $b,c,d$ in A.P.$\Rightarrow b+d=2c$

Again $a,c,e$ are also in A.P. $\therefore a+e=2c$

$\therefore E=2c-4\left(2c\right)+6c=8c-8c=0$