Question

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

Answer 1

Answer:

Let x be the common difference of the A.P. a,b,c,d,e,f.

As e is the 5th term

∴e=a+(5−1)x(∵a

n

=a+(n−1)d), where a_n is the nth term

⇒e=a+4x ...(1)

and c=a+2x ...(2)

∴ Using equation (1) and (2), we get

e−c=a+4x−a−2x

⇒e−c=2x=2(d−c)

Answer 2

Let x be the common difference of the A.P.

a, b, c, d, e, f.

As e is the 5th term .

e = a + (5-1)x (an = a + (n − 1)d),

where a_n is the nth term

⇒ e = a + 4x ...(1)

and c = a + 2x ...(2) ...

Using equation (1) and (2), we get

e-c = a + 4x - a - 2x

⇒ e c = 2x = 2(d - c)