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What is the next term of the arithmetic sequence? -8,-3,2,7,12", "

What is the next term of the arithmetic sequence?−8,−3,2,7,12-8,-3,2,7,12

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Full solution

Q. What is the next term of the arithmetic sequence?−8,−3,2,7,12-8,-3,2,7,12
  1. Identify if arithmetic: Identify if the given sequence is arithmetic.\newlineTo determine if a sequence is arithmetic, we check if the difference between consecutive terms is constant.
  2. Calculate common difference: Calculate the common difference in the sequence.\newlineThe difference between the first two terms is −3−(−8)=5-3 - (-8) = 5.\newlineThe difference between the next two terms is 2−(−3)=52 - (-3) = 5.\newlineSince the difference is the same, the sequence is arithmetic with a common difference of 55.
  3. Find next term: Find the next term in the arithmetic sequence.\newlineTo find the next term, add the common difference to the last term in the sequence.\newlineThe last term given is 1212, so we calculate 12+5=1712 + 5 = 17.

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