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Ta có: 98 +102 + 106 + .... + n = 15050
=> (2 + 6 + 10 + ... + n) - (2 + 6 + 10 + ... + 94) = 15050
Ta có số số hạng là: (n - 2) : 4 + 1 = (n - 2) : 4 + 4 : 4 = (n - 2 + 4) : 4 = (n + 2) : 4
=> (n + 2) x (n + 2) : 8 - (94 + 2) x 24 : 2 = 15050
=> (n + 2) x (n + 2) : 8 = 15050 + 1152
=> (n + 2) x (n + 2) = 16202 x 8 = 129616 (1)
Vì n thuộc số tự nhiên nên suy ra: Không có giá trị n nào thỏa mãn (1).
![](https://rs.olm.vn/images/avt/0.png?1311)
Áp dụng công thức tính dãy số ta có:
\(\frac{\left[\left(x-98\right):4+1\right].\left(x+98\right)}{2}=15050\)
\(\Rightarrow\left(\frac{x-98}{4}+1\right).\left(x+98\right)=30100\)
\(\Rightarrow\left(\frac{x-98+4}{4}\right)\left(x+98\right)=30100\)
\(\Rightarrow\left(\frac{x+94}{4}\right)\left(x+98\right)=30100\)
\(\Rightarrow\frac{x+94}{4}x+\frac{x+94}{4}.98=30100\)
\(\Rightarrow\frac{x^2+94x}{4}+\frac{98x+9212}{4}=30100\)
\(\Rightarrow x^2+192x+9212=120400\)
\(\Rightarrow x^2+192x=111188\)
\(\Rightarrow x.\left(x+192\right)=111188\)
\(\Rightarrow x=252\)
số số hạng là (x-98):4+1=x/4-49/2+1=x/4-47/2=(x-94)/4
tổng là (x+98).(x-94)/4:2=(x+98).(x-94)/2=15050
=>(x+98).(x-94)=30100
đến đây tớ xin bái
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\(102+\left(26-3.x\right):5=106\)
\(\left(26-3x\right):5=106-102=4\)
\(26-3x=4.5=20\)
\(3x=26-20=6\)
\(x=6:3=2\)
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`-7/6=x/18`
`=>-21/18=x/18`
`=>x=-21(TM\ x in Z)`
`-7/6=-98/y`
`=>-98/84=-98/y`
`=>y=84(TM\ y in Z)`
`-7/6=-14/z`
`=>-14/12=-14/z`
`=>z=12(TM\ z in Z)`
`-7/6=t/102`
`=>-119/102=t/102`
`=>t=-119(TM\ t in Z)`
Vậy `(x,y,z,t)=(-21,84,12,-119)`
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(x+1)+(x+2)+........+(x+100) = 15050
100x + 100.(100+1):2 = 15050
100x + 5050 = 15050
100x = 15050 - 5050 = 10000
x = 10000 : 100 = 100
( x + 1) + ( x + 2 ) + ( x + 3 ) + ........+ ( x + 100 ) = 15050
100x + 100 . ( 100 +1 ) : 2 = 15050
100x = 15050 -5050
100 x = 10 000
x= 10 000 : 100
x= 100
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{-7}{6}=\frac{x}{18}=\frac{-98}{y}=\frac{-14}{z}=\frac{t}{102}=\frac{u}{-18}\)
\(\text{+) }\frac{-7}{6}=\frac{x}{18}\)
\(\Rightarrow\left(-7\right).18=6.x\)
\(\Rightarrow-126=6.x\)
\(\Rightarrow x=-21\)
\(\text{+) }\frac{-7}{6}=\frac{-98}{y}\)
\(\Rightarrow\left(-7\right).y=6.\left(-98\right)\)
\(\Rightarrow y=\frac{6.\left(-98\right)}{-7}\)
\(\Rightarrow y=-84\)
\(\text{+) }\frac{-7}{6}=\frac{-14}{z}\)
\(\Rightarrow\left(-7\right).z=\left(-14\right).6\)
\(\Rightarrow\left(-7\right).z=-84\)
\(\Rightarrow z=12\)
\(\frac{-7}{6}=\frac{t}{102}\)
\(\Rightarrow\left(-7\right).102=t.6\)
\(\Rightarrow t=\frac{\left(-7\right).102}{6}=\frac{\left(-7\right).17.6}{6}\)
\(\Rightarrow t=-119\)
\(\frac{-7}{6}=\frac{u}{-18}\)
\(\Rightarrow\frac{-7}{6}=\frac{-u}{18}\)
\(\Rightarrow\left(-7\right).18=\left(-u\right).6\)
\(\Rightarrow-126=\left(-u\right).6\)
\(\Rightarrow-u=-21\)
\(\Rightarrow u=21\)