Arithmetic mean relation

If the arithmetic mean of the numbers a1, a2, a3, a4, and a5 is the number A, the arithmetic mean of the numbers a1, a2, a3, and a4 is the number B, then what is a5 equal to?

Final Answer:

a₅ = 5A-4B

Step-by-step explanation:

$$\begin{gathered} A=\frac{a_1+a_2+a_3+a_4+a_5}{5} \\ B=\frac{a_1+a_2+a_3+a_4}{4} \\ 5A=a_1+a_2+a_3+a_4+a_5 \\ 4B=a_1+a_2+a_3+a_4 \\ 5A-4B=a_1+a_2+a_3+a_4+a_5-(a_1+a_2+a_3+a_4) \\ {a}_5=5A-4B \end{gathered}$$

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