TIP
To Insert two arithmetic means between -12 and 18
means -12, a, b, 18
STEP 1 OUT 5
a,b is the inserted arithemetic means.
Let the common differences be d
d=a-(-12).....(i)
d=b-a.....(ii)
d=18-b....(iii)
STEP 2 OUT 5
substitute for the value of d in equation (i) using d=b-a
b-a=a-(-12)
collect the like terms
b=a+a+12
b=2a+12.....(iv)
STEP 3 OUT 5
substitute for the value of d in equation (iii) using d=b-a
b-a=18-b
collect the like terms
b+b=a+18
2b=a+18........(v)
STEP 4 OUT 5
We can now solve equation (iv) and equation (v) simultaneously
b=2a+12.....(iv)
2b=a+18.....(v)
we can substitute for b in equation (v)
2(2a+12)= a+18
4a+24=a+18
collect the like terms
4a-a=18-24
3a=-6
Divide both sides by 3
a= -2
STEP 5 OUT 5
Now let's find b we can use either equation (iv) or (v)
using equation (iv). we have to substitute for a
b=2(-2)+12
b=-4+12
b=8
THE FINAL ANSWER IS -2,8
THE TWO ARITHMETIC MEANS BETWEEN -12 AND 18 ARE;
-2, 8