If a, b, c, d, e are in A.P.,then the value o | vedclass

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(D) Let the common difference of the $A.P.$ be $d_0$.Then,$b = a + d_0$,$c = a + 2d_0$,$d = a + 3d_0$,and $e = a + 4d_0$.Substitute these values into

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None of these

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(D) Let the common difference of the $A.P.$ be $d_0$.Then,$b = a + d_0$,$c = a + 2d_0$,$d = a + 3d_0$,and $e = a + 4d_0$.Substitute these values into the expression $a + b + 4c - 4d + e$:$= a + (a + d_0) + 4(a + 2d_0) - 4(a + 3d_0) + (a + 4d_0)$$= a + a + d_0 + 4a + 8d_0 - 4a - 12d_0 + a + 4d_0$$= (a + a + 4a - 4a + a) + (d_0 + 8d_0 - 12d_0 + 4d_0)$$= 3a + (1 + 8 - 12 + 4)d_0$$= 3a + 1d_0$$= 3a + d_0$Since the expression depends on the common difference $d_0$,it cannot be expressed solely in terms of $a$ unless $d_0$ is known. Therefore,the correct option is $D$.

If $a, b, c, d, e$ are in $A.P.$,then the value of $a + b + 4c - 4d + e$ in terms of $a$,if possible,is:

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