Find the 65^("th ") term of the arithmetic sequence -26,-11,4,dots Answer:

Use Formula: To find the 65th 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 -26.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 = -11 - (-26) = -11 + 26 = 15Calculate 65th Term: Now that we have the first term and the common difference, we can find the 65th term (a_65) using the formula: a_65 = a_1 + (65 - 1)dSubstitute Values: Substitute the known values into the formula: a_65 = -26 + (65 - 1) * 15Perform Calculation: Perform the calculation: a_65 = -26 + (64 * 15) a_65 = -26 + 960 a_65 = 934

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Find the
65^("th ") term of the arithmetic sequence
-26,-11,4,dots
Answer:

Find the $65^{\text {th }}$ term of the arithmetic sequence $-26,-11,4, \ldots$ $\newline$ Answer:

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Algebra 2

Composition of linear and quadratic functions: find an equation

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Q. Find the

65^{\text {th }}

term of the arithmetic sequence

-26,-11,4, \ldots

\newline

Answer:

Use Formula: To find the $65^{th}$ 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 $-26$ .
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: $d = -11 - (-26) = -11 + 26 = 15$
Calculate $65$ th Term: Now that we have the first term and the common difference, we can find the $65$ th term ( $a_{65}$ ) using the formula: $\newline$ $a_{$65$} = a_1 + ($65$ - $1$)d
Substitute Values: Substitute the known values into the formula: $a_{65} = -26 + (65 - 1) \times 15$
Perform Calculation: Perform the calculation:$\newline$$a_{65} = -26 + (64 \times 15)$$\newline$$a_{65} = -26 + 960$$\newline$$a_{65} = 934$