Find the 100th term of the arithmetic sequence -9,-19,-29,dots Answer:

Arithmetic Sequence Formula: To find the 100th term of an arithmetic sequence, we 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, identify the first term (a_1) of the sequence. In this case, the first term is -9.Determine Common Difference: Next, determine the common difference (d) of the sequence. The common difference is the difference between any two consecutive terms. Here, the second term is -19 and the first term is -9, so the common difference is -19 - (-9) = -10.Find 100th Term: Now, apply the formula to find the 100th term (a_100). We have a_1 = -9, n = 100, and d = -10. Plugging these values into the formula gives us a_100 = -9 + (100 - 1)(-10).Calculate Inside Parentheses: Perform the calculation inside the parentheses first: 100 - 1 = 99.Multiply by Common Difference: Now multiply 99 by the common difference, -10: 99 * -10 = -990.Add First Term: Finally, add the first term to this product to find the 100th term: a_100 = -9 + (-990) = -999.

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Find the 100th term of the arithmetic sequence
-9,-19,-29,dots
Answer:

Find the $100$ th term of the arithmetic sequence $-9,-19,-29, \ldots$ $\newline$ Answer:

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Q. Find the

100

th term of the arithmetic sequence

-9,-19,-29, \ldots

\newline

Answer:

Arithmetic Sequence Formula: To find the $100^{\text{th}}$ term of an arithmetic sequence, we use the formula for the $n^{\text{th}}$ term of an arithmetic sequence, which is $a_n = a_1 + (n - 1)d$ , where $a_n$ is the $n^{\text{th}}$ 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, identify the first term ( $a_1$ ) of the sequence. In this case, the first term is $-9$ .
Determine Common Difference: Next, determine the common difference $d$ of the sequence. The common difference is the difference between any two consecutive terms. Here, the second term is $-19$ and the first term is $-9$ , so the common difference is $-19 - (-9) = -10$ .
Find $100$ th Term: Now, apply the formula to find the $100$ th term $a_{100}$ . We have $a_1 = -9$ , $n = 100$ , and $d = -10$ . Plugging these values into the formula gives us $a_{100} = -9 + (100 - 1)(-10)$ .
Calculate Inside Parentheses: Perform the calculation inside the parentheses first: $100 - 1 = 99$ .
Multiply by Common Difference: Now multiply $99$ by the common difference, $-10$ : $99 \times -10 = -990$ .
Add First Term: Finally, add the first term to this product to find the $100^{\text{th}}$ term: $a_{100} = -9 + (-990) = -999$ .