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Find the 66th term of the arithmetic sequence
-27,-41,-55,dots
Answer:

Find the $66$ th term of the arithmetic sequence $-27,-41,-55, \ldots$ $\newline$ Answer:

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Decimal numbers review

Full solution

Q. Find the

66

th term of the arithmetic sequence

-27,-41,-55, \ldots

\newline

Answer:

Identify common difference: Identify the common difference in the arithmetic sequence. $\newline$ The common difference $d$ is the difference between any two consecutive terms. We can find it by subtracting the first term from the second term. $\newline$ $d = -41 - (-27) = -41 + 27 = -14$
Use formula for nth term: Use the formula for the nth term of an arithmetic sequence. $\newline$ The nth term $a_n$ of an arithmetic sequence can be found using the formula: $\newline$ $a_n = a_1 + (n - 1)d$ $\newline$ where $a_1$ is the first term, $n$ is the term number, and $d$ is the common difference.
Plug values for $66$ th term: Plug the values into the formula to find the $66^{th}$ term. $\newline$ $a_1 = -27$ (the first term) $\newline$ $n = 66$ (the term number we want to find) $\newline$ $d = -14$ (the common difference found in Step $1$ ) $\newline$ Now, calculate the $66^{th}$ term using the formula: $\newline$ $a_{66} = -27 + (66 - 1)(-14)$
Perform calculations: Perform the calculations. $\newline$ $a_{66} = -27 + (65)(-14)$ $\newline$ $a_{66} = -27 - 910$ $\newline$ $a_{66} = -937$

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