Question

a b c d e f are in A.P then find the value of a^(2)-b^(2)+c^(2)-d^(2)+e^(2)-f^(2) having common difference D=-1 .​

Answer 1

Step-by-step explanation:

Let the common difference is x

so.

\begin{lgathered}a + x = b \\ a + 2x = c \\ a + 3x = d \\ a + 4x = e \\ a + 5x = f \\ now \\ e - c = a + 4x - a - 2x \\ e - c = 2x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - 1 \\ and \\ d - c = a + 3x - a - 2x \\ d - c = x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - 2 \\ from \: 1and \: 2 \: \: we \: get \\ e - c = 2(d - c)\end{lgathered}a+x=ba+2x=ca+3x=da+4x=ea+5x=fnowe−c=a+4x−a−2xe−c=2x−1andd−c=a+3x−a−2xd−c=x−2from1and2wegete−c=2(d−c)

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