# if 3, b, -1, c are terms of an A.P, then find b and c

hala718 | Certified Educator

3, b , -1 , c    are terms of an Arthematical progression.

Let r be the common difference:

Then we know that:

b = 3 + r.........(1)

-1 = 3 + 2r........(2)

c = 3 + 3r...........(3)

Let us solve equation (2) to determine r:

-1 = 3 + 2r

==> 2r= -4

==> r= -2

Then the common difference r = -2

Now let us substitue in (1):

b= 3+ r = 3+ -2 = 1

==> b = 1

Now we will substitute in (3):

c = 3 + 3r

c = 3+ 3*-2

==> c = 3-6 = -3

==> c = -3

Then the series will be:

3, 1, -1, -3   is an A.P where r = -2 is the common difference

neela | Student

If  a1, a2 and  a3 are the consecutive terms of an AP, then

2a2 = a1+a3.

Twice middle term a2 = a1 +a2.

Given that  3, b, -1, c are the terms (assumed consecutive terms) of an AP.

Therefore  for the first 3 terms 2b = (3+1). So b= 4/2 = 2.

Having determined b = 2, for the second 3 terms: b, -1 , c or  2, -1, c, we have:

2*(-1) = b+c= 2+c.

-2 = 2+c.

So c = -2 -2 = -4.

Therefore c = -4,

So,  b = -1 and c = -4.