Find the 77^("th ") term of the arithmetic sequence 14,3,-8,dots Answer:

Use Arithmetic Sequence Formula: To find the 77th term of an arithmetic sequence, we need to use the formula for the nth term of an arithmetic sequence, which 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 between the terms.Identify First Term: First, we identify the first term $ a_1 $ of the sequence, which is given as 14.Find Common Difference: Next, we need to find the common difference $ d $. We can do this by subtracting the second term from the first term: \[ d = 3 - 14 \] \[ d = -11 \]Calculate 77th Term: Now that we have the first term and the common difference, we can find the 77th term $ a_{77} $ using the formula: \[ a_{77} = a_1 + (77 - 1)d \] \[ a_{77} = 14 + (76)(-11) \]We perform the multiplication and addition to find $ a_{77} $: \[ a_{77} = 14 + (76)(-11) \] \[ a_{77} = 14 - 836 \] \[ a_{77} = -822 \]

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Find the
77^("th ") term of the arithmetic sequence
14,3,-8,dots
Answer:

Find the $77^{\text {th }}$ term of the arithmetic sequence $14,3,-8, \ldots$ $\newline$ Answer:

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Q. Find the

77^{\text {th }}

term of the arithmetic sequence

14,3,-8, \ldots

\newline

Answer:

Use Arithmetic Sequence Formula: To find the $77$ th term of an arithmetic sequence, we need to use the formula for the nth term of an arithmetic sequence, which is given by: $\newline$ $a_n = a_1 + (n - 1)d$ $\newline$ 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 $14$ .
Find Common Difference: Next, we need to find the common difference $d$ . We can do this by subtracting the second term from the first term: $\newline$ $d = 3 - 14$ $\newline$ $d = -11$
Calculate $77$ th Term: Now that we have the first term and the common difference, we can find the $77$ th term $a_{77}$ using the formula: $\newline$ $a_{77} = a_1 + (77 - 1)d$ $\newline$ $a_{77} = 14 + (76)(-11)$
Calculate $77$ th Term: Now that we have the first term and the common difference, we can find the $77$ th term $a_{77}$ using the formula: $\newline$ $a_{77} = a_1 + (77 - 1)d$ $\newline$ $a_{77} = 14 + (76)(-11)$ We perform the multiplication and addition to find $a_{77}$ : $\newline$ $a_{77} = 14 + (76)(-11)$ $\newline$ $a_{77} = 14 - 836$ $\newline$ $a_{77} = -822$