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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$2(d - c)$

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

Similar Questions

The number of terms in an $A.P.$ is even. The sum of the odd terms is $24$ and the sum of the even terms is $30$. If the last term exceeds the first term by $10\frac{1}{2}$,then the number of terms in the $A.P.$ is:

Find the $9^{th}$ term of the $H.P. 6, 4, 3, \ldots$

The roots of the equation $x^5 - 40x^4 + px^3 + qx^2 + rx + s = 0$ are in $G.P.$ The sum of their reciprocals is $10$. Then the value of $|s|$ is

If $2^{10} + 2^{9} \cdot 3^{1} + 2^{8} \cdot 3^{2} + \ldots + 2^{0} \cdot 3^{10} = S - 2^{11}$,then $S$ is equal to

If the $7^{th}$ term of a $H.P.$ is $\frac{1}{10}$ and the $12^{th}$ term is $\frac{1}{25}$,then the $20^{th}$ term is

Vedclass Test Series

Exam Paper Generator

Online Exam Module