Арифметическая прогрессия содержит 8 членов. Сумма членов, стоящих на четных мес...

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Арифметическая прогрессия содержит 8 членов. Сумма членов, стоящих на четных местах, равна 28, а на нечетных местах 16,Найдите разность прогрессии

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Матов

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По условию
$a_{2}+a_{4}+a_{6}+a_{8}=28\\
a_{1}+a_{3}+a_{5}+a_{7}=16\\
\\
a_{1}+d+a_{1}+3d+a_{1}+5d+a_{1}+7d=28\\
a_{1}+a_{1}+2d+a_{1}+4d+a_{1}+6d=16\\
\\
4a_{1}+16d=28\\
4a_{1}+12d=16\\
\\
28-16d=16-12d\\
12=4d\\
d=3$
Ответ разность равна 3

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