Key Concepts
- Calculating the mean
- Solving algebraic equations
To find the mean of a set of numbers, we find their sum and divide it by the number of terms there are.
Solving the Question
We're given:
- The mean of (a + 1) + (a + 4) + (a + 7) + (a + 8) + (a + 10) is 12
- Find a
The sum of (a + 1) + (a + 4) + (a + 7) + (a + 8) + (a + 10) divided by 5 (because there are 5 numbers) is 12. Write this as an equation:
[tex]12=\dfrac{(a + 1) + (a + 4) + (a + 7) + (a + 8) + (a + 10)}{5}[/tex]
Simplify:
[tex]12=\dfrac{a + 1 + a + 4 + a + 7 + a + 8 + a + 10}{5}\\\\12=\dfrac{5a + 30}{5}\\\\12=a +6\\a=6[/tex]
Answer
a = 6
