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Find the 87 th term of the arithmetic sequence
-26,-11,4,dots
Answer:

Find the $87$ th term of the arithmetic sequence $-26,-11,4, \ldots$ $\newline$ Answer:

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Solve exponential equations using logarithms

Full solution

Q. Find the

87

th term of the arithmetic sequence

-26,-11,4, \ldots

\newline

Answer:

Question Prompt: Question prompt: What is the $87$ th term of the arithmetic sequence $-26, -11, 4, \ldots$ ?
Identify Common Difference: Identify the common difference $d$ of the arithmetic sequence by subtracting the first term from the second term. $\newline$ $d = -11 - (-26)$ $\newline$ $d = -11 + 26$ $\newline$ $d = 15$
Use Formula for nth Term: Use the formula for the nth term of an arithmetic sequence: $a_n = a_1 + (n - 1)d$ , where $a_n$ is the nth term, $a_1$ is the first term, and $d$ is the common difference. $\newline$ We need to find the $87$ th term ( $a_{87}$ ), so $n = 87$ , $a_1 = -26$ , and $d = 15$ .
Substitute Values: Substitute the values into the formula to find the $87^{th}$ term. $a_{87} = -26 + (87 - 1) \times 15$ $a_{87} = -26 + (86 \times 15)$
Calculate Inside Parentheses: Calculate the value inside the parentheses first. $86 \times 15 = 1290$
Substitute Calculated Value: Now, substitute the calculated value back into the equation. $a_{87} = -26 + 1290$
Perform Addition: Perform the addition to find the $87$ th term. $\newline$ $a_{87} = 1264$

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