Answer:
Third number is 12
Step-by-step explanation:
Let [tex]\displaystyle \large{d}[/tex] be common difference & [tex]\displaystyle \large{x}[/tex] be the third number. Set up the following equations:
[tex]\displaystyle \large{x-2d=-2 \to (1)}\\\\\displaystyle \large{x+2d=26 \to (2)}[/tex]
Solve the simultaneous equation for x-term:
[tex]\displaystyle \large{2x=24}\\\\\displaystyle \large{x=12}[/tex]
Let’s make sure that we get accurately answer. Substitute x = 12 in any equations which I’ll choose (1):
[tex]\displaystyle \large{12-2d=-2}\\\\\displaystyle \large{-2d=-14}\\\\\displaystyle \large{d=7}[/tex]
Now add each terms with common difference as 7:
-2+7 = 5
5+7 = 12
12+7 = 19
19+7 = 26
So our pattern is -2, 5, 12, 19, 26. Since the question only asks for third number then the answer is 12
