Question

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

Answer 1

A = 18
-3 = 18 + 3d
-3-18 = 3d
-21/3 = d
d =-7
a = A + d
a = 18 +(-7)
a = 11
b = 18 +2(-7)
b = 18-14
b = 4

Answer 2

Since 18,a,b,-3 are in A.P
so,
a-18=b-a
2a-b=18.... (i)

b-a=-3-b
a-2b=3 ..... (ii)

multiply (i) by 2 and Substract with (ii)

4a-2b-a+2b= 36-3
3a=33
a=11

Put a=11 in (ii)
11-2b=3
2b=8
b=4
Hence
a+b=11+4=15