Find the 89th term of the arithmetic sequence -10,-28,-46,dots Answer:

Identify common difference: Identify the common difference in the arithmetic sequence. The sequence is -10, -28, -46, ... To find the common difference, subtract the first term from the second term: -28 - (-10) = -28 + 10 = -18.Use formula for nth term: Use the formula for the nth term of an arithmetic sequence. The nth term of an arithmetic sequence is given by a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference.Plug values for 89th term: Plug the values into the formula to find the 89th term. a_1 = -10 (the first term), n = 89 (since we're looking for the 89th term), and d = -18 (the common difference). So, a_89 = -10 + (89 - 1)(-18).Perform calculations: Perform the calculations. a_89 = -10 + (88)(-18) a_89 = -10 - 1584 a_89 = -1594

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Grade 7

Decimal numbers review

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Q. Find the

89

th term of the arithmetic sequence

-10,-28,-46, \ldots

\newline

Answer:

Identify common difference: Identify the common difference in the arithmetic sequence. $\newline$ The sequence is $-10$ , $-28$ , $-46$ , ... $\newline$ To find the common difference, subtract the first term from the second term: $-28 - (-10) = -28 + 10 = -18$ .
Use formula for nth term: Use the formula for the nth term of an arithmetic sequence. $\newline$ The nth term of an arithmetic sequence is given by $a_n = a_1 + (n - 1)d$ , where $a_n$ is the nth term, $a_1$ is the first term, $n$ is the term number, and $d$ is the common difference.
Plug values for $89$ th term: Plug the values into the formula to find the $89^{th}$ term. $\newline$ $a_1 = -10$ (the first term), $n = 89$ (since we're looking for the $89^{th}$ term), and $d = -18$ (the common difference). $\newline$ So, $a_{89} = -10 + (89 - 1)(-18)$ .
Perform calculations: Perform the calculations. $\newline$ $a_{89} = -10 + (88)(-18)$ $\newline$ $a_{89} = -10 - 1584$ $\newline$ $a_{89} = -1594$