Предмет: Алгебра, автор: ANGELINOCHKA96

Найдите 15-ый член и сумму первых пятнадцати членов прогрессии 2;5;8... .

Ответы

Автор ответа: hote

дана прогрессия
2;5;8

Найдем разность этой арифметической прогрессии
d= 5-2= 3
d=8-5=3

Значит d=3

по формуле n- члена найдем а(15)

$displaystyle a_{15}=a_1+d*(15-1)=d_1+14d\\a_{15}=2+3*14=44$

найдем сумму 15 членов

$displaystyle S_{15}= frac{a_1+a_{15}}{2}*15\\S_{15}= frac{2+44}{2}*15= 23*15=345$

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