Find the 51 st term of the arithmetic sequence 21,6,-9,dots Answer:

Given values: To find the 51st term of an arithmetic sequence, we need to know the first term (a1) and the common difference (d). The first term a1 is given as 21.Calculate common difference: The common difference (d) can be found by subtracting the second term from the first term. So, d = 6 - 21.Use nth term formula: Calculating the common difference, we get d = -15.Substitute values: The formula to find the nth term of an arithmetic sequence is an = a1 + (n - 1)d. We will use this formula to find the 51st term (a51).Calculate (n-1): Substituting the known values into the formula, we get a51 = 21 + (51 - 1)(-15).Multiply by common difference: Calculating the term inside the parentheses first, we have (51 - 1) = 50.Add first term: Now, we multiply 50 by the common difference, which is -15. So, 50 * (-15) = -750.Calculate final result: Finally, we add the first term to the product of the common difference and (n - 1), which gives us a51 = 21 + (-750).Calculating the sum, we find that a51 = 21 - 750 = -729.

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Find the 51 st term of the arithmetic sequence
21,6,-9,dots
Answer:

Find the $51$ st term of the arithmetic sequence $21,6,-9, \ldots$ $\newline$ Answer:

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Grade 8

Evaluate variable expressions for sequences

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Q. Find the

51

st term of the arithmetic sequence

21,6,-9, \ldots

\newline

Answer:

Given values: To find the $51^{\text{st}}$ term of an arithmetic sequence, we need to know the first term ( $a_1$ ) and the common difference ( $d$ ). The first term $a_1$ is given as $21$ .
Calculate common difference: The common difference $d$ can be found by subtracting the second term from the first term. So, $d = 6 - 21$ .
Use nth term formula: Calculating the common difference, we get $d = -15$ .
Substitute values: The formula to find the $n$ th term of an arithmetic sequence is $a_n = a_1 + (n - 1)d$ . We will use this formula to find the $51$ st term ( $a_{51}$ ).
Calculate $(n-1)$ : Substituting the known values into the formula, we get $a_{51} = 21 + (51 - 1)(-15)$ .
Multiply by common difference: Calculating the term inside the parentheses first, we have $(51 - 1) = 50$ .
Add first term: Now, we multiply $50$ by the common difference, which is $-15$ . So, $50 \times (-15) = -750$ .
Calculate final result: Finally, we add the first term to the product of the common difference and $n - 1$ , which gives us $a_{51} = 21 + (-750)$ .
Calculate final result: Finally, we add the first term to the product of the common difference and $n - 1$ , which gives us $a_{51} = 21 + (-750)$ .Calculating the sum, we find that $a_{51} = 21 - 750 = -729$ .