Question

if 9,a,b-6 are in ap then a+b=​

Answer 1

Answer:

a+b=21

Step-by-step explanation:

Given : 9, a, b,-6 are in AP.

To find : The value of a+b?

Solution :

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

We know, common difference are constant.

So, $a - 27 = b - a = -6 - b$

i.e. $2a - b = 27$  ----------(1)

$2b - a = -6$ ----------(2)

Solve (1) and (2),

Multiply (2) by 2 and add  (1),

$2a - b+4b-2a = 27-12$

$3b= 15$

$b=5$

Put b in equation (1),

$2a - 5 = 27$

$2a=32$

$a=16$

Now, a=16 and b=5

$a+b=16+5=21$

Answer 2

a + b = 3  if 9 , a  , b  ,  -  6  are in AP

Step-by-step explanation:

9 , a  , b  ,  -  6  are in AP

=> a - 9  = b - a  =  - 6  - b

=> a - 9 = b - a

=> 2a = b + 9

b - a = -6 - b

=> 2b  = a - 6

Adding both

2a + 2b = b + 9 + a - 6

=> a + b = 3

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