If 18, a, b, −3 are in A.P., the a + b =

Solution:

Here, we are given four terms which are in A.P.,

First term (a1) = 

Second term (a2) = 

Third term (a3) = 

Fourth term (a4)= 

So, in an A.P. the difference of two adjacent terms is always constant. So, we get,

$d=a_{2}-a_{1}$

$d=a-18$$\ldots \ldots$ (1)

Also,

$d=a_{4}-a_{3}$

 

$d=-3-b$.......$(2)$

Now, on equating (1) and (2), we get,

$a-18=-3-b$

$a+b=18-3$

$a+b=15$

Therefore, $a+b=15$

Hence the correct option is (d).