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Find three numbers in A.P. whose sum is ...

Find three numbers in A.P. whose sum is 21 and the product of last two numbers is 63.

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To solve the problem of finding three numbers in Arithmetic Progression (A.P.) whose sum is 21 and the product of the last two numbers is 63, we can follow these steps: ### Step 1: Define the three numbers in A.P. Let the three numbers be: - First number: \( a - d \) - Second number: \( a \) - Third number: \( a + d \) ### Step 2: Set up the equation for the sum of the numbers. According to the problem, the sum of these three numbers is 21: \[ (a - d) + a + (a + d) = 21 \] This simplifies to: \[ 3a = 21 \] ### Step 3: Solve for \( a \). Dividing both sides by 3: \[ a = \frac{21}{3} = 7 \] ### Step 4: Set up the equation for the product of the last two numbers. The product of the last two numbers is given as 63: \[ a \cdot (a + d) = 63 \] Substituting \( a = 7 \): \[ 7 \cdot (7 + d) = 63 \] ### Step 5: Solve for \( d \). Dividing both sides by 7: \[ 7 + d = \frac{63}{7} = 9 \] Subtracting 7 from both sides: \[ d = 9 - 7 = 2 \] ### Step 6: Find the three numbers. Now that we have \( a = 7 \) and \( d = 2 \), we can find the three numbers: - First number: \( a - d = 7 - 2 = 5 \) - Second number: \( a = 7 \) - Third number: \( a + d = 7 + 2 = 9 \) Thus, the three numbers are: \[ 5, 7, 9 \] ### Final Answer: The three numbers in A.P. are **5, 7, and 9**. ---

To solve the problem of finding three numbers in Arithmetic Progression (A.P.) whose sum is 21 and the product of the last two numbers is 63, we can follow these steps: ### Step 1: Define the three numbers in A.P. Let the three numbers be: - First number: \( a - d \) - Second number: \( a \) - Third number: \( a + d \) ...
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Knowledge Check

  • Find three numbers in G.P.whose sum is 52 and the sum of whose products pairs is 624.

    A
    2, 12, 32
    B
    2,12, 72
    C
    4, 12, 36
    D
    None of these
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