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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). 457,448,439,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).\newline457,448,439,… 457,448,439, \ldots \newlineFind the 4141st term.\newlineAnswer:

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Full solution

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).\newline457,448,439,… 457,448,439, \ldots \newlineFind the 4141st term.\newlineAnswer:
  1. Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. The given sequence decreases by the same amount each time, which suggests it is an arithmetic sequence.
  2. Calculate Common Difference: Calculate the common difference of the sequence.\newlineThe difference between the first two terms is 448−457=−9448 - 457 = -9.\newlineThe difference between the second and third terms is 439−448=−9439 - 448 = -9.\newlineThe common difference is −9-9.
  3. Use Arithmetic Sequence Formula: Use the arithmetic sequence formula to find the 41st41^{st} term.\newlineThe nthn^{th} term of an arithmetic sequence is given by the formula: an=a1+(n−1)da_n = a_1 + (n - 1)d, where ana_n is the nthn^{th} term, a1a_1 is the first term, nn is the term number, and dd is the common difference.
  4. Substitute Values and Solve: Substitute the known values into the formula to find the 41st41^{st} term.\newlinea41=457+(41−1)(−9)a_{41} = 457 + (41 - 1)(-9)\newlinea41=457+40(−9)a_{41} = 457 + 40(-9)\newlinea41=457−360a_{41} = 457 - 360\newlinea41=97a_{41} = 97

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