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The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary). 5,14,23,dots Find the 43rd term. Answer:

The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary).\newline5,14,23,… 5,14,23, \ldots \newlineFind the 4343rd term.\newlineAnswer:

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Q. The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary).\newline5,14,23,… 5,14,23, \ldots \newlineFind the 4343rd term.\newlineAnswer:
  1. Determine Pattern: First, we need to determine the pattern of the sequence. We can do this by finding the difference between consecutive terms.\newlineDifference between second and first term: 14−5=914 - 5 = 9\newlineDifference between third and second term: 23−14=923 - 14 = 9
  2. Arithmetic Sequence: Since the difference between consecutive terms is constant, we have an arithmetic sequence with a common difference of 99.
  3. Formula for nth Term: To find the nnth term of an arithmetic sequence, we use the formula:\newlinenth term=first term+(n−1)×common difference\text{nth term} = \text{first term} + (n - 1) \times \text{common difference}
  4. Calculate 4343rd Term: We are looking for the 43rd43^{rd} term, so we plug in the values into the formula:\newline43rd43^{rd} term =5+(43−1)×9= 5 + (43 - 1) \times 9
  5. Calculate 4343rd Term: We are looking for the 43rd43^{rd} term, so we plug in the values into the formula:\newline43rd43^{rd} term =5+(43−1)×9= 5 + (43 - 1) \times 9Now we calculate the term:\newline43rd43^{rd} term =5+(42×9)= 5 + (42 \times 9)\newline43rd43^{rd} term =5+378= 5 + 378\newline43rd43^{rd} term =383= 383

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