Find the 72 nd term of the arithmetic sequence -23,-39,-55,dots Answer:

Arithmetic Sequence Formula: To find the 72nd term of an arithmetic sequence, we need to use the formula for the nth term of an arithmetic sequence, which is: 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 between the terms.Identify First Term: First, we identify the first term (a_1) of the sequence, which is given as -23.Find Common Difference: Next, we need to find the common difference (d). We can do this by subtracting the first term from the second term: d = -39 - (-23) = -39 + 23 = -16Calculate 72nd Term: Now that we have the first term and the common difference, we can find the 72nd term (a_72) using the formula: a_72 = a_1 + (72 - 1)dSubstitute Values: Substitute the known values into the formula: a_72 = -23 + (72 - 1)(-16) a_72 = -23 + (71)(-16)Perform Calculation: Now, perform the multiplication and addition to find a_72: a_72 = -23 + (-1136) a_72 = -1159

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Find the
72 nd term of the arithmetic sequence
-23,-39,-55,dots
Answer:

Find the $72 n d$ term of the arithmetic sequence $-23,-39,-55, \ldots$ $\newline$ Answer:

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Grade 8

Sequences: mixed review

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Q. Find the

72 n d

term of the arithmetic sequence

-23,-39,-55, \ldots

\newline

Answer:

Arithmetic Sequence Formula: To find the $72^{nd}$ term of an arithmetic sequence, we need to use the formula for the $n^{th}$ term of an arithmetic sequence, which is: $\newline$ $a_n = a_1 + (n - 1)d$ $\newline$ where $a_n$ is the $n^{th}$ term, $a_1$ is the first term, $n$ is the term number, and $d$ is the common difference between the terms.
Identify First Term: First, we identify the first term $a_1$ of the sequence, which is given as $-23$ .
Find Common Difference: Next, we need to find the common difference $d$ . We can do this by subtracting the first term from the second term: $\newline$ $d = -39 - (-23) = -39 + 23 = -16$
Calculate $72$ nd Term: Now that we have the first term and the common difference, we can find the $72$ nd term $a_{72}$ using the formula: $\newline$ $a_{72} = a_1 + (72 - 1)d$
Substitute Values: Substitute the known values into the formula: $\newline$ $a_{72} = -23 + (72 - 1)(-16)$ $\newline$ $a_{72} = -23 + (71)(-16)$
Perform Calculation: Now, perform the multiplication and addition to find $a_{72}$ : $\newline$ $a_{72} = -23 + (-1136)$ $\newline$ $a_{72} = -1159$