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What is the next term of the arithmetic sequence? -4,-9,-14,-19", "

What is the next term of the arithmetic sequence?−4,−9,−14,−19-4,-9,-14,-19

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Full solution

Q. What is the next term of the arithmetic sequence?−4,−9,−14,−19-4,-9,-14,-19
  1. Identify sequence type: Identify the type of sequence.\newlineThe sequence −4-4, −9-9, −14-14, −19-19 has a constant difference between its terms, which indicates that it is an arithmetic sequence.
  2. Determine common difference: Determine the common difference of the sequence.\newlineTo find the common difference, subtract the first term from the second term: −9−(−4)=−5-9 - (-4) = -5.
  3. Verify common difference: Verify the common difference with another pair of consecutive terms.\newlineSubtract the third term from the fourth term: −19−(−14)=−5-19 - (-14) = -5. This confirms that the common difference is indeed −5-5.
  4. Calculate next term: Calculate the next term in the sequence.\newlineTo find the next term, add the common difference to the last given term: −19+(−5)=−24-19 + (-5) = -24.

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