Math, asked by thinknoodles202, 1 year ago

if a, b, c, d, e, f, are in A.P., then e-c is equal to:

Answers

Answered by MonarkSingh

199

$\huge\boxed{\texttt{\fcolorbox{Red}{aqua}{Hey Mate!!!!}}}$

$<b>$
Given - a, b, c, d, e and f are in A.P

Let the common difference is x

so.
$a + x = b \\ a + 2x = c \\ a + 3x = d \\ a + 4x = e \\ a + 5x = f \\ now \\ e - c = a + 4x - a - 2x \\ e - c = 2x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - 1 \\ and \\ d - c = a + 3x - a - 2x \\ d - c = x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - 2 \\ from \: 1and \: 2 \: \: we \: get \\ e - c = 2(d - c)$
$\large{\red{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\underline{\underline{\underline{Hope\:it\:helps\: you}}}}}}}}}}}}}}}$

Answered by MonarkSinghD

$\huge\boxed{\texttt{\fcolorbox{Red}{Blue}{Hey Mate!!!!}}}$

$<b><body bgcolor="yellow">$ Given that
a, b, c, d, e and f are in A.P.

Let the common difference be x.

So,
$a + x = b \\ a + 2x = c \\ a + 3x = d \\ a + 4x = e \\ a + 5x = f$
Now,
$e - c = a + 4x - a - 2x \\ e - c = 2x \: \: \: \: \: \: \: \: \: \: \: \: - - - - - 1$
And,
$d - c = a + 3x - a - 2x \\ \\ d - c = x \: \: \: \: \: \: \: \: \: \: \: - - - - - - 2$
From equation 1 and 2,
$e - c = 2(d - c)$

$\large{\green{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\underline{\underline{\underline{Hope\:it\:helps\: you}}}}}}}}}}}}}}}$