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For the following A.P.'s write the first...

For the following A.P.'s write the first term and the common difference:
`3,-1,-3….`

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The correct Answer is:
To solve the problem, we need to identify the first term and the common difference of the given sequence: `3, -1, -3, ...`. ### Step-by-Step Solution: 1. **Identify the First Term (A1)**: The first term of the sequence is the first number in the list. \[ A_1 = 3 \] 2. **Identify the Second Term (A2)**: The second term of the sequence is the second number in the list. \[ A_2 = -1 \] 3. **Identify the Third Term (A3)**: The third term of the sequence is the third number in the list. \[ A_3 = -3 \] 4. **Calculate the Common Difference (D)**: The common difference in an arithmetic progression (A.P.) is found by subtracting the first term from the second term or the second term from the third term. - First, calculate the difference between the second term and the first term: \[ D_1 = A_2 - A_1 = -1 - 3 = -4 \] - Next, calculate the difference between the third term and the second term: \[ D_2 = A_3 - A_2 = -3 - (-1) = -3 + 1 = -2 \] 5. **Conclusion**: Since the common differences \(D_1\) and \(D_2\) are not equal (\(-4\) and \(-2\)), the sequence does not have a constant common difference. Therefore, it is not an arithmetic progression (A.P.). ### Final Answer: - First Term (A1): \(3\) - Common Difference (D): Not applicable (the sequence is not an A.P.)
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OSWAL PUBLICATION-ARITHMETIC PROGRESSIONS -NCERT CORNER (EXERCISE-5.1)
  1. Write first four terms of the A. P., when the first term a and the com...

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  2. Write first four terms of the A. P., when the first term a and the com...

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  3. For the following A.P.'s write the first term and the common differenc...

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  4. For the following A.P.'s write the first term and the common differenc...

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  5. For the following A.P.'s write the first term and the common differenc...

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  6. For the following A.P.'s write the first term and the common differenc...

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  7. Which of the following are AP's ? If they form an A. P. , find the com...

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  8. Which of the following are AP's ? If they form an A. P. , find the com...

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  9. Which of the following are AP's ? If they form an A. P. , find the com...

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  10. Which of the following are AP's ? If they form an A. P. , find the com...

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  11. Which of the following are AP's ? If they form an A. P. , find the com...

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  12. Which of the following are AP's ? If they form an A. P. , find the com...

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  13. Which of the following are AP's ? If they form an A. P. , find the com...

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  14. Which of the following are AP's ? If they form an A. P. , find the com...

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  15. Which of the following are AP's ? If they form an A. P. , find the com...

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  16. Which of the following are AP's ? If they form an A. P. , find the com...

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  17. Which of the following are AP's ? If they form an A. P. , find the com...

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  18. Which of the following are AP's ? If they form an A. P. , find the com...

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  19. Which of the following are AP's ? If they form an A. P. , find the com...

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  20. Which of the following are AP's ? If they form an A. P. , find the com...

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