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

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

(a) 19

(b) 7

(c) 11

(d) 15

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).