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

Identify common difference: Identify the common difference in the arithmetic sequence. 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. d = -41 - (-27) = -41 + 27 = -14 Use formula for nth term: Use the formula for the nth term of an arithmetic sequence. The nth term (a_n) of an arithmetic sequence can be found using the formula: a_n = a_1 + (n - 1)d where a_1 is the first term, n is the term number, and d is the common difference. Plug values for 66th term: Plug the values into the formula to find the 66th term. a_1 = -27 (the first term) n = 66 (the term number we want to find) d = -14 (the common difference found in Step 1) Now, calculate the 66th term using the formula: a_66 = -27 + (66 - 1)(-14) Perform calculations: Perform the calculations. a_66 = -27 + (65)(-14) a_66 = -27 - 910 a_66 = -937

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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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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. $\newline$ $a_{66} = -27 + (65)(-14)$ $\newline$ $a_{66} = -27 - 910$ $\newline$ $a_{66} = -937$