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Find the common difference of the arithmetic sequence -9,-16,-23,dots Answer:

Find the common difference of the arithmetic sequence −9,−16,−23,… -9,-16,-23, \ldots \newlineAnswer:

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Full solution

Q. Find the common difference of the arithmetic sequence −9,−16,−23,… -9,-16,-23, \ldots \newlineAnswer:
  1. Find Common Difference: To find the common difference of an arithmetic sequence, we subtract any term from the term that follows it.\newlineLet's subtract the first term from the second term: −16−(−9)-16 - (-9).
  2. Subtract First Term: Now, we perform the subtraction: −16−(−9)=−16+9=−7-16 - (-9) = -16 + 9 = -7. This is the common difference of the sequence.
  3. Verify Common Difference: To verify that this is indeed the common difference, we can subtract the second term from the third term: −23−(−16)-23 - (-16).
  4. Verify Common Difference: To verify that this is indeed the common difference, we can subtract the second term from the third term: −23−(−16)-23 - (-16).Performing the subtraction gives us: −23−(−16)=−23+16=−7-23 - (-16) = -23 + 16 = -7. This confirms that the common difference is consistent across the terms we've checked.

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