Find the 91st term of the arithmetic sequence -25,-39,-53,dots Answer:

Use nth term formula: To find the 91st 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. From the given sequence, the first term is -25.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: \[ d = -39 - (-25) \] \[ d = -39 + 25 \] \[ d = -14 \]Calculate 91st term: Now that we have the first term and the common difference, we can find the 91st term $ a_{91} $ using the formula: \[ a_{91} = a_1 + (91 - 1)d \] \[ a_{91} = -25 + (90)(-14) \] \[ a_{91} = -25 - 1260 \] \[ a_{91} = -1285 \]

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Q. Find the

91

st term of the arithmetic sequence

-25,-39,-53, \ldots

\newline

Answer:

Use nth term formula: To find the $91$ st 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. From the given sequence, the first term is $-25$ .
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: $\newline$ $d = -39 - (-25)$ $\newline$ $d = -39 + 25$ $\newline$ $d = -14$
Calculate $91$ st term: Now that we have the first term and the common difference, we can find the $91$ st term $a_{91}$ using the formula: $\newline$ $a_{91} = a_1 + (91 - 1)d$ $\newline$ $a_{91} = -25 + (90)(-14)$ $\newline$ $a_{91} = -25 - 1260$ $\newline$ $a_{91} = -1285$