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

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(C) Given that $a, b, c, d, e, f$ are in $A.P.$Let the common difference be $K$.Then,$b - a = c - b = d - c = e - d = f - e = K$.We need to find the v

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$2(d - c)$

Vedclass · Answer

(C) Given that $a, b, c, d, e, f$ are in $A.P.$Let the common difference be $K$.Then,$b - a = c - b = d - c = e - d = f - e = K$.We need to find the value of $e - c$.Since $d - c = K$ and $e - d = K$,we have $e - d = d - c$.Adding $d$ to both sides,we get $e = 2d - c$.Therefore,$e - c = (2d - c) - c = 2d - 2c = 2(d - c)$.Alternatively,using the property of $A.P.$,$e = c + 2K$ and $d = c + K$.Thus,$e - c = (c + 2K) - c = 2K$.Since $d - c = K$,$2K = 2(d - c)$.Hence,$e - c = 2(d - c)$.

If $a, b, c, d, e, f$ are in $A.P.$,then the value of $e - c$ will be

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