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

Find the $89$ th term of the arithmetic sequence $-10,-28,-46, \ldots$ $\newline$ Answer:

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Decimal numbers review

Full solution

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. $\newline$ $a_{89} = -10 + (88)(-18)$ $\newline$ $a_{89} = -10 - 1584$ $\newline$ $a_{89} = -1594$

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