Find the 75^("th ") term of the arithmetic sequence 13,33,53,dots Answer:

Identify common difference: Identify the common difference in the arithmetic sequence. The sequence is 13, 33, 53, ... where each term increases by 20. Common difference (d) = 33 - 13 = 20Use formula for nth term: Use the formula for the nth term of an arithmetic sequence. The nth term (a_n) of an arithmetic sequence is given by a_n = a_1 + (n - 1)d, where a_1 is the first term and d is the common difference.Substitute values for 75th term: Substitute the values into the formula to find the 75th term. a_1 = 13 (the first term) n = 75 (since we are looking for the 75th term) d = 20 (the common difference) a_75 = 13 + (75 - 1) * 20Perform calculations: Perform the calculations. a_75 = 13 + (74 * 20) a_75 = 13 + 1480 a_75 = 1493

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Find the
75^("th ") term of the arithmetic sequence
13,33,53,dots
Answer:

Find the $75^{\text {th }}$ term of the arithmetic sequence $13,33,53, \ldots$ $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

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Q. Find the

75^{\text {th }}

term of the arithmetic sequence

13,33,53, \ldots

\newline

Answer:

Identify common difference: Identify the common difference in the arithmetic sequence. $\newline$ The sequence is $13, 33, 53, \ldots$ where each term increases by $20$ . $\newline$ Common difference $(d) = 33 - 13 = 20$
Use formula for nth term: Use the formula for the nth term of an arithmetic sequence. $\newline$ The nth term $a_n$ of an arithmetic sequence is given by $a_n = a_1 + (n - 1)d$ , where $a_1$ is the first term and $d$ is the common difference.
Substitute values for $75$ th term: Substitute the values into the formula to find the $75^{th}$ term. $\newline$ $a_1 = 13$ (the first term) $\newline$ $n = 75$ (since we are looking for the $75^{th}$ term) $\newline$ $d = 20$ (the common difference) $\newline$ $a_{75} = 13 + (75 - 1) \times 20$
Perform calculations: Perform the calculations. $\newline$ $a_{75} = 13 + (74 \times 20)$ $\newline$ $a_{75} = 13 + 1480$ $\newline$ $a_{75} = 1493$