Tìm tổng 1+4+7+......+28
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Tổng (21 + x) \( \vdots \) 7. Mà 21 \( \vdots \) 7 nên x cũng \( \vdots \) 7.
Mà x \( \in \) {1; 14; 16; 22; 28} nên x = 14 hoặc x = 28.
![](https://rs.olm.vn/images/avt/0.png?1311)
A/ \(\frac{4}{5}+\frac{1}{5}x=\left(-\frac{1}{28}\right)\)
\(\frac{1}{5}x=\left(-\frac{1}{28}\right)-\frac{4}{5}\)
\(\frac{1}{5}x=\left(-\frac{5}{140}\right)-\frac{112}{140}\)
\(\frac{1}{5}x=-\frac{117}{140}\)
\(x=\left(-\frac{117}{140}\right):\frac{1}{5}\)
\(x=\left(-\frac{117}{28}\right)\)
B/ \(\left(\frac{3x}{7}+1\right):\left(-4\right)=-\frac{1}{28}\)
\(\frac{3x}{7}+1=\left(-\frac{1}{28}\right).\left(-4\right)\)
\(\frac{3x}{7}+1=\frac{1}{7}\)
\(\frac{3x}{7}=\frac{1}{7}-1\)
\(\frac{3x}{7}=\frac{1}{7}-\frac{7}{7}\)
\(\frac{3x}{7}=-\frac{6}{7}\)
\(\Rightarrow3x=\left(-6\right)\)(theo cách l8)
\(\Rightarrow x=\left(-6\right):3=\left(-2\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a. \(\frac{4}{5}+\frac{1}{5}x=\frac{1}{28}\)
\(\Leftrightarrow\frac{1}{5}x=\frac{1}{28}-\frac{4}{5}\)
\(\Leftrightarrow\frac{1}{5}x=\frac{5}{140}-\frac{112}{140}\)
\(\Leftrightarrow\frac{1}{5}x=\frac{-107}{140}\)
\(\Leftrightarrow x=\frac{-107}{140}\div\frac{1}{5}\)
\(\Leftrightarrow x=\frac{-107}{140}\times5\)
\(\Leftrightarrow x=\frac{-107}{28}=\)
b. \(\left(\frac{3x}{7}+1\right)\div\left(-4\right)=\frac{-1}{28}\)
\(\Leftrightarrow\left(\frac{3x}{7}+\frac{7}{7}\right)=\frac{-1}{28}\times\left(-4\right)\)
\(\Leftrightarrow\frac{3x+1}{7}=\frac{1}{7}\)
\(\Leftrightarrow3x+1=1\)
\(\Leftrightarrow3x=1-1\)
\(\Leftrightarrow3x=0\Leftrightarrow x=0\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Sửa đề: 7/4+7/28+...+7/550
=7/1*4+7/4*7+7/7*10+...+7/22*25
=7/3(1-1/4+1/4-1/7+...+1/22-1/25)
=7/3*24/25=56/25
![](https://rs.olm.vn/images/avt/0.png?1311)
Phân số thứ 2 là:
( \(\frac{28}{5}\)\(-\) \(\frac{7}{4}\)) \(:\) \(2\) = \(\frac{77}{40}\)
Đ/s:. .......
~ Hok T ~
Phân số thứ hai là:
\(\left(\frac{28}{5}-\frac{7}{4}\right)\div2=\frac{77}{40}\)
Đáp số: \(\frac{77}{40}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{3x}{7+1}:\left(-4\right)=\frac{-1}{28}\)
\(\frac{3x}{7+1}\)=\(\frac{-1}{28}.\left(-4\right)\)
\(\frac{3x}{7+1}\)=\(\frac{1}{7}\)
\(\frac{3x}{8}\)=\(\frac{1}{7}\)
\(3x\)=\(\frac{8.1}{7}\)=\(\frac{8}{7}\)
\(x\)=\(\frac{8}{7}\): \(3\)
\(x\)=\(\frac{8}{21}\)
ta thấy tổng 1 + 4 + 7 + .... + 28 có ( 28 - 1 ) : 3 +1=10 số hạng
=> 1 + 4 + 7 + ... + 28 = ( 28 + 1 ) * 10 : 2
= 145
SSH là : ( 28 - 1 ) : 3 + 1 = 10
S của dãy số là : ( 28 + 1 ) . 10 : 2 = 145