Question

The average of 5 consecutive numbers is n. if the next two numbers are also included, the average of the 7 numbers will be

Answer 1

Answer:

$\red { Average \: 7 \: consecutive \: numbers}\green {= n+1}$

Step-by-step explanation:

$Let \: x ,(x+1),(x+2),(x+3) \:and \: (x+4)\:are \\ first \: 5 \: consecutive \: numbers$

$Average \:of \: 5 \: consecutive \: numbers = n$

$\frac{sum \: of \:the \: numbers }{5} = n$

$\implies \frac{x+x+1+x+2+x+3+x+4}{5} = n$

$\implies \frac{5x+10}{5} = n$

$\implies \frac{5(x+2)}{5} = n$

$\implies x+2 = n$

$\implies x = n - 2 \: ---(1)$

$Now, \: If \: next \: two \: numbers \:included ,\\then$

$Average \: 7 \: consecutive \: numbers \\= \frac{x+x+1+x+2+x+3+x+4+x+5+x+6}{7}\\= \frac{7x+21}{7}\\=\frac{7(x+3)}{7}\\=x+3 \\= n-2+3 \:[From \: (1)]\\= n + 1$

Therefore.,

$\red { Average \: 7 \: consecutive \: numbers}\green {= n+1}$

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