Question

if 9 , a , b and -6 are in ap find a +b

Answer 1

Answer:

3

Step-by-step explanation:

Since 9, a, b, -6 are in AP

therefore, a - 9 = b - a  ----(1)

Similarly, b - a = -6 - b ----(2)

From (1) and (2)

a - 9 = -6 - b

a + b = -6 + 9

a + b = 3

Answer 2

Answer:

The required value is 3.

Step-by-step explanation:

Given :

9, a, b and -6 are in A.P

To find :

the value of (a + b)

Solution :

In an A.P, the difference between the term and it's preceding term is constant.

So,

a - 9 = b - a = -6 - b

⇒ a - 9 = -6 - b

⇒ a = -6 - b + 9

⇒ a = 3 - b

⇒ a + b = 3

∴ The value of (a + b) is 3

_____________________________

Arithmetic Progression :

• It is the sequence of numbers such that the difference between any two successive numbers is constant.

• In AP,

       a - first term  

       d - common difference  

       aₙ - nth term  

       Sₙ - sum of n terms  

• General form of AP,

          a , a+d , a+2d , a+3d , ...  

• nth term of AP,

        aₙ = a + (n - 1)d

• Sum of first n terms in A.P,  

      $\longmapsto \sf S_n=\dfrac{n}{2}[2a+(n-1)d]$