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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). 310,304,298,dots Find the 41st 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).\newline310,304,298,… 310,304,298, \ldots \newlineFind the 4141st 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).\newline310,304,298,… 310,304,298, \ldots \newlineFind the 4141st term.\newlineAnswer:
  1. Determine common difference: First, we need to determine the common difference of the sequence by subtracting any term from the previous term.\newlineCommon difference = 304−310304 - 310
  2. Calculate common difference: Now, let's calculate the common difference.\newlineCommon difference = 304−310=−6304 - 310 = -6
  3. Use nth term formula: Next, we use the formula for the nth term of an arithmetic sequence, which is:\newlinenth term = first term + (n−1)×common difference(n - 1) \times \text{common difference}\newlineWe want to find the 41st41^{\text{st}} term, so n=41n = 41.
  4. Substitute values: Let's substitute the values into the formula to find the 41st41^{\text{st}} term.41st41^{\text{st}} term = 310+(41−1)×(−6)310 + (41 - 1) \times (-6)
  5. Calculate inside parentheses: Now, we calculate the term inside the parentheses and then multiply by the common difference.\newline41st41^{\text{st}} term = 310+(40)×(−6)310 + (40) \times (-6)
  6. Perform multiplication: Next, we perform the multiplication. 41st41^{\text{st}} term = 310+(−240)310 + (-240)
  7. Add numbers: Finally, we add the numbers to find the 41st41^{st} term.\newline41st41^{st} term =310−240=70= 310 - 240 = 70

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