Question

Варифметической прогрессии а7/а2=5 s8=120 a1-? d-?

Answer 1

$S_8= \frac{2a_1+7d}{2}\cdot8$

По условию
$\frac{2a_1+7d}{2}\cdot8 =120$
2а₁+7d=30
$\frac{a_7}{a_2}= \frac{a_1+6d}{a_1+d}$
По условию
$\frac{a_1+6d}{a_1+d}=5 \\ \\ a_1+6d=5(a_1+d) \\ \\ 4a_1=d 2a_1+7d=30 \\ \\ 2a_1+28a_1=30\\ \\30a_1=30\\ \\a_1=1 \\ \\ d=4$

Answer 2

$\frac{a_7}{a_2}=5 \\ S_8=120 \\ a_1=?,d=? \\ a_7=5a_2 \iff a_1+6d=5(a_1+d)=5a_1+5d \\ d=4a_1 \\ S_8= \frac{a_1+a_1+7d}{2}*8=120 \\ 4(2a_1+7d)=120 \iff 2a_1+7d=30 \\ \left \{ {{d=4a_1} \atop {2a_1+7d=30}} \right. \\ 2a_1+7*4a_1=30 \\ 30a_1=30 \iff a_1=1 \\ d=4a_1=4*1=4 \\ a_1=1;d=4$