Question

if a,b and -3 are in AP,then find a+b

Answer 1

a,b,-3 are in A.P.
So...
$\frac{a + ( - 3)}{2} = b$
$\frac{a - 3}{2} = b$
$a - 3 = 2b$
$a + 2b = 3$
Also,
if common difference is d
b= a+d => a=b-d
-3= a+2d => a=-3-2d
a+2b=3
b-d+2b=3
3b=3+d
b=1+1/3d*
a+b= -3-2d+1+1/3d
a+b= -2-7/3d.... (1)
a+2b= 3.... (2)
by subtracting (1) from (2)
b =5+7/3d
*b=1+1/3d
5+7/3d =1+1/3d
4= -6/3 d
4= -2d
d= -2
so, a= -3-2d & 3b=3+d
a= -3-2(-2) & 3b=3-2
a= -3+4 & 3b=1
a= 1 & b=1/3
a+b = 1+1/3
a+b = 4/3....Ans.