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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). 13,26,52,dots Find the 6th 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).\newline13,26,52,… 13,26,52, \ldots \newlineFind the 66th 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).\newline13,26,52,… 13,26,52, \ldots \newlineFind the 66th term.\newlineAnswer:
  1. Identify Pattern: Identify the pattern in the sequence.\newlineThe given sequence is 1313, 2626, 5252, ...\newlineWe notice that each term is double the previous term.
  2. Determine Sequence Type: Determine the type of sequence.\newlineSince each term is double the previous term, this is a geometric sequence with a common ratio rr of 22.
  3. Find First Term: Find the first term (a1a_1) of the sequence.\newlineThe first term of the sequence is given as 1313.
  4. Use Formula for nth Term: Use the formula for the nth term of a geometric sequence.\newlineThe nth term of a geometric sequence is given by an=a1⋅r(n−1)a_n = a_1 \cdot r^{(n-1)}.
  5. Calculate 66th Term: Calculate the 66th term using the formula.\newlinea6=13×26−1a_6 = 13 \times 2^{6-1}\newlinea6=13×25a_6 = 13 \times 2^5\newlinea6=13×32a_6 = 13 \times 32\newlinea6=416a_6 = 416
  6. Round to Nearest Thousandth: Round the 66th term to the nearest thousandth if necessary.\newlineSince the 66th term is a whole number, no rounding is necessary.

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