Question

if a,b,c,d,e,f are in ap then prove that e-c=f-b​

Answer 1

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) a+x=ba+2x=ca+3x=da+4x=ea+5x=

now−c=a+4x−a−2xe−c=2x−1andd−c=a+3x−a−2xd−c=x−2

from1and2wegete−c=2(d−c)