Find the 71 st term of the arithmetic sequence 1,17,33,dots Answer:

Arithmetic Sequence Formula: To find the 71st 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 1.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 = 17 - 1 = 16Calculate 71st Term: Now that we have the first term and the common difference, we can find the 71st term (a_71) using the formula: a_71 = a_1 + (71 - 1)dSubstitute Values: Substitute the known values into the formula: a_71 = 1 + (71 - 1) * 16Perform Calculation: Perform the calculation inside the parentheses first: a_71 = 1 + (70 * 16)Multiply Values: Now, multiply 70 by 16: a_71 = 1 + 1120Add to Find 71st Term: Finally, add 1 to 1120 to find the 71st term: a_71 = 1121

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Find the 71 st term of the arithmetic sequence
1,17,33,dots
Answer:

Find the $71$ st term of the arithmetic sequence $1,17,33, \ldots$ $\newline$ Answer:

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Grade 7

Evaluate variable expressions for Sequences

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Q. Find the

71

st term of the arithmetic sequence

1,17,33, \ldots

\newline

Answer:

Arithmetic Sequence Formula: To find the $71^{st}$ 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 $1$ .
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: $d = 17 - 1 = 16$
Calculate $71$ st Term: Now that we have the first term and the common difference, we can find the $71$ st term $a_{71}$ using the formula: $\newline$ $a_{71} = a_1 + (71 - 1)d$
Substitute Values: Substitute the known values into the formula: $a_{71} = 1 + (71 - 1) \times 16$
Perform Calculation: Perform the calculation inside the parentheses first: $a_{71} = 1 + (70 \times 16)$
Multiply Values: Now, multiply $70$ by $16$ : $a_{71} = 1 + 1120$
Add to Find $71$ st Term: Finally, add $1$ to $1120$ to find the $71st$ term: $\newline$ $a_{71} = 1121$