Consecutive numbers

Sum of ten consecutive numbers is 105. Determine these numbers (write first and last).

Correct answer:

a₁ =  6
a₁₀ =  15

Step-by-step explanation:

$$\begin{gathered} d=1 \\ {s}_{10}=105 \\ {s}_{10}=10(a_1+a_{10})\mathrm{/}2\cdot d \\ 210=10(a_1+a_{10}) \\ 21=a_1+a_{10}=a_1+a_1+9 \\ 12=2a_1 \\ {a}_1=12\mathrm{/}2=6 \end{gathered}$$

$a_{10}=6+(10-1)\cdot 1=15$

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