算術線上測驗

以下測驗提供了與基礎算術相關的多項選擇題 (MCQ)。您需要閱讀所有給出的答案，然後點選正確的答案。如果您不確定答案，可以使用顯示答案按鈕檢視答案。您可以使用下一題按鈕檢視測驗中的新一組問題。

第 1 題 - 等差數列 4, 4.5, 5, 5.5 ... 的第 105 項是多少？

答案：A

解釋

Here a = 4, d = 4.5 - 4 = 0.5, n = 105 
Using formula T_n = a + (n - 1)d 
T₁₀₅ = 4 + (105 - 1) x 0.5 
= 56

第 2 題 - 除數是商的五倍，也是餘數的五倍。如果餘數是 29，則被除數是多少？

答案：B

解釋

  
Divisor = (5 x 29) = 145 = 5 x Quotient = Divisor 
=> Quotient = 145/5 = 29 
Dividend = (Divisor x Quotient) + Remainder 
Dividend = (145* 29) + 29 = 4234.

第 3 題 - 最小的質數是多少？

答案：B

解釋

2 是最小的質數。

第 4 題 - 兩個數分別比第三個數少 50% 和 54%。第二個數比第一個數少百分之幾？

答案：D

解釋

 
 Let the third number be 100. 
 ∴First Number = 50 and Second Number = 46 
 Decrease = 50 - 46 = 4 
 ∴Required Percentage = (4/50)x100 = 8%

第 5 題 - 如果等差數列 a, a-b, a-2b, ... 的第 10 項是 20，第 20 項是 10，那麼第 x 項是多少？

答案：D

解釋

  
 Here a = a-b,  d = (a-2b) - (a-b) = -b,    
 Using formula T_n = a + (n - 1)d    
 T₁₀ = (a-b) + (10 - 1) x (-b) = 20    
 => a - 9b = 20 ... (i) 
 T₂₀ = (a-b) + (20 - 1) x (-b) = 10    
 => a - 19b = 10 ... (ii) 
 Subtracting (ii) from (i) 10b = 10 
 => b = 1 
 Using (i) a - 9(1) = 20 
 => a = 29 
 ∴ x^th term = a + (x-1)d 
 = a + (x-1)(-b) = 20 + (x-1)(-1) 
 = 30-x

第 6 題 - 如果 a, a-2 和 3a 成等差數列，那麼 a 是多少？

答案：B

解釋

 
 As a, a-2 and 3a are in an A.P. 
 ∴ (a-2) - a = 3a - (a-2) 
 => -2 = 2a - 2 
 => a = -2

第 7 題 - 等比數列中三個數的和是 28，它們的積是 512。這三個數是多少？

答案：C

解釋

   
 let the numbers are a/r, a, ar  
 Then a/r x a x ar = 512  
 => a³ = 8³  
 gt; a = 8  
 Now a/r + a + ar = 28  
 => 8/r + 8 + 8r = 28  
 => 8/r + 8r = 20  
 => 2/r + 2r = 5  
 => 2r² + -5r + 2 = 0  
 => 2r² + -4r -r + 2 = 0  
 => 2r(r-2) - (r-2)=0  
 => (r-2)(2r-1) = 0  
 => r = 2 or r = 1/2  
 ∴ numbers are 4, 8, 16.

第 8 題 - 在一個俱樂部中，會員的年齡成等差數列，公差為 3 個月。如果最年輕的會員是 7 歲，所有會員年齡的總和是 250 歲，那麼俱樂部有多少名會員？

答案：C

解釋

   
 let the ages be 7 , 7.25, 7.5 and so on  
 Here a = 7, d = 1/4 , S_n = 250   
 Using formula S_n = (n/2)[2a + (n-1)d]   
 => (n/2)[14+(n-1)(1/4)]  = 250  
 => n[14 + (n-1)/4] = 500  
 => n[56 + (n-1)] = 2000  
 => n[n + 55] = 2000  
 => n² + 55n - 2000 = 0  
 => n² + 80n -25n - 2000 = 0  
 => n(n-80) -25(n-80) = 0  
 => (n-80)(n-25) = 0  
 => n = 25

第 9 題 - 2, 7, 12, 17... 中的哪一項是 92？

答案：D

解釋

  
 Here a = 2,  d = 7 - 2 = 5,  
 Let there be n term.  
 Using formula T_n = a + (n - 1)d  
 T_n = 2 + (n - 1) x 5 = 92  
 => 5n - 3 = 92  
 => n = 19

第 10 題 - 如果一個等差數列的第 4 項是 16，第 12 項是 80。它的第 17 項是多少？

答案：A

解釋

  
 Let's have first term as a, common difference is d then  
 a + 3d = 16 ... (i)  
 a + 11d = 80 ... (ii)  
 Subtracting (i) from (ii)  
 => 8d = 64  
 => d = 8  
 Using (i)  
 => a = 14 - 3d  = -10 
 Using formula T_n = a + (n - 1)d    
 T₁₇ = -10 + (17 - 1) x 8
 = 118

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