# What is the value of a and b, given that 4+a, 8, 10b and a+2b are terms of AP

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

In an arithmetic progression, the difference between consecutive terms is the same. We use this property to build up two equations that can be solved to arrive at a and b.

10b - 8 = 8 - (4+a)

=> 10b – 8 = 8 – 4 – a

=> a = 12 – 10b … (1)

a+2b – 10b = 10b -8

=> a – 8b = 10b - 8

=> a = 18b - 8 … (2)

Equating the values of a from (1) and (2), we get

12 – 10b = 18b – 8

=> 28b = 20

=> b = 20/28 = 5/7

Now substitute b = 5/7 which we have determined earlier in (1)

a = 12 – 10*(5/7)

=> a = 12 – 50/7

=> a = 34/7

Therefore the required values of a and b are 34/7 and 5/7 respectively.

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

4+ a , 8, 10b, a+2b  are terms of an Arthematical progression:

Let (r) be the common difference:

Then we know that:

a1= 4+a

8 = (4+a) + r...........(1)

10b = (4+a) + 2r........(2)

a+ 2b= (4+a) + 3r.........(3)

Let us solve the system:

First we will rewrtie:

a + r = 4 . ==> a = 4-r...........(4)

10b = 4+ a + 2r

Substutue in with a:

==> 10b = 4 + (4-r)  + 2r

==> 10b = 8 + r

==> r = 10b - 8..................(5)

a+2b = (4+a) + 3r

(4-r) + 2b = 4 + 4-r + 3r

2b =  4 + 3r .................(6)

2b = 4 + (10b-8)

2b = 4 + 10b  - 8

==> -8b = -4

==> b= 1/2

==> r = 10b- 8

==> r= 5 - 8 = -3

==> r= -3

==> a = 4- r = 4 --3 = 7

==> a = 7

neela | High School Teacher | (Level 3) Valedictorian

Posted on

We suppose the terms , 4+a,8,10b, and a+2b are the consecutive terms of an arithmetic progressio.

So the  difference of the duccessive terms must be equal to the common difference d.

8-(4+a) = 10b-8 .

4-a = 10b -8

-a-10b = = -8-4 = -12

a+10b = 12...(1).

Also

8-(4+a) = a+2b-10b.Or

4-a = a-8b

-a-a+8b = -4.

-2a+8b = -4

We divide by 2:

-a+4b = -2.....(2).

Eq(1)+eq(2) gives: 10b+4b = = 12-2 = 10.

14b = 10.

b= 10/14 = 5/7.

Put b= 1 in (2): -a +4*5/7 = -2.

-a = -2- 4*5/7 = -34/7

a =  34/7.

Therefore a= 34/7 and b = 5/7.