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The sum of three number in arithmetic progression is 21 and their products is 231. Find the numbers?
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The sum of three number in arithmetic progression is 21 and their prod...
Given:
- Sum of the three numbers in arithmetic progression = 21
- Product of the three numbers = 231
Let the three numbers be:
- \( a-d \)
- \( a \)
- \( a+d \)
where \( a \) is the middle term and \( d \) is the common difference.
Find the numbers:
Step 1: Express the sum in terms of a and d
Given that the sum of the three numbers is 21, we have:
\[ (a-d) + a + (a+d) = 21 \]
\[ 3a = 21 \]
\[ a = 7 \]
Step 2: Express the product in terms of a and d
Given that the product of the three numbers is 231, we have:
\[ (a-d) \times a \times (a+d) = 231 \]
\[ (7-d) \times 7 \times (7+d) = 231 \]
\[ 49 - d^2 = 33 \]
\[ d^2 = 16 \]
\[ d = 4 \]
Step 3: Find the numbers
Substitute the values of a and d back into the expressions:
- First number = \( a-d = 7-4 = 3 \)
- Second number = \( a = 7 \)
- Third number = \( a+d = 7+4 = 11 \)
Therefore, the three numbers in the arithmetic progression are 3, 7, and 11.
- Sum of the three numbers in arithmetic progression = 21
- Product of the three numbers = 231
Let the three numbers be:
- \( a-d \)
- \( a \)
- \( a+d \)
where \( a \) is the middle term and \( d \) is the common difference.
Find the numbers:
Step 1: Express the sum in terms of a and d
Given that the sum of the three numbers is 21, we have:
\[ (a-d) + a + (a+d) = 21 \]
\[ 3a = 21 \]
\[ a = 7 \]
Step 2: Express the product in terms of a and d
Given that the product of the three numbers is 231, we have:
\[ (a-d) \times a \times (a+d) = 231 \]
\[ (7-d) \times 7 \times (7+d) = 231 \]
\[ 49 - d^2 = 33 \]
\[ d^2 = 16 \]
\[ d = 4 \]
Step 3: Find the numbers
Substitute the values of a and d back into the expressions:
- First number = \( a-d = 7-4 = 3 \)
- Second number = \( a = 7 \)
- Third number = \( a+d = 7+4 = 11 \)
Therefore, the three numbers in the arithmetic progression are 3, 7, and 11.
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The sum of three number in arithmetic progression is 21 and their products is 231. Find the numbers?
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The sum of three number in arithmetic progression is 21 and their products is 231. Find the numbers? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The sum of three number in arithmetic progression is 21 and their products is 231. Find the numbers? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of three number in arithmetic progression is 21 and their products is 231. Find the numbers?.
The sum of three number in arithmetic progression is 21 and their products is 231. Find the numbers? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The sum of three number in arithmetic progression is 21 and their products is 231. Find the numbers? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of three number in arithmetic progression is 21 and their products is 231. Find the numbers?.
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