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(x+1)+(2x+3)+(3x+5)+...+(50x+99)=3775
=> (x + 2x + 3x + ... + 50x) + (1 + 3 + 5 + ... + 99) = 3775
=> x . (1 + 2 +3 + ...+ 50) + (1 + 3 + 5 + ... + 99) = 3775
Áp dụng công thức tính dãy số ta có :
\(1+2+3+...+50=\frac{\left[\left(50-1\right):1+1\right].\left(50+1\right)}{2}=\frac{50.51}{2}=25.51=1275\)
\(1+3+5+...+99=\frac{\left[\left(99-1\right):2+1\right].\left(99+1\right)}{2}=\frac{50.100}{2}=50.50=2500\)
=> x . 1275 + 2500 = 3775
=> 1275x = 1275
=> x = 1
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(x + 1) + (x + 2) + ... + (x + 100) = 102x
x + x + x + ... + x + 1 + 2 + ... + 100 = 102x
100x + (100 + 1) x 100 : 2 = 102x
102x - 100x = 5050
2x = 5050
x = 2525
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a) x+2x+...+50x =2550
x. [ 1+2+3+....+50]=2550
ta co :
so so hang cua day 1;2;3;4;...;50:
[50-1]:1+1=50
tong cua day tren la :
[50+1].50:2=1275
=> x.1275=2550
x=2550:1275
vay x=2
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(x+1) + (x+2) +...+(x+99) = 6138
=> 1+2+...+99 + 99x = 6138
=> 100 x 99 : 2 + 99x = 6138
=>4950 + 99x = 6138
=> 99x = 6138 - 4950
=> 99x = 1188
=> x = 1188 :99
=> x = 12
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Ta có \(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+99\right)=50x\)
\(\Rightarrow100x+\left(1+2+3+....+99\right)=50x\)
\(\Rightarrow100x+4950=50x\)
\(\Rightarrow-50x=4950\)
\(\Rightarrow x=-99\)
x + x + 1 + ... + x + 99 = 50x
Có số số hạng là : ( 99 - 1 ) : 1 + 1 = 99 ( số )
Tổng là : ( 99 + 1 ) . 99 : 2 = 4950
=> 100x + 4950 = 50x
4950 = -50x
=> x = -99
Vậy,........