Answer :

Sure, let's find the 81st term of the arithmetic sequence [tex]\(-10, -25, -40, \ldots\)[/tex].

1. Identify the first term and the common difference:
- The first term ([tex]\(a_1\)[/tex]) of the sequence is [tex]\(-10\)[/tex].
- The common difference ([tex]\(d\)[/tex]) is the difference between any two consecutive terms. Thus, [tex]\(d\)[/tex] can be calculated as:
[tex]\[
d = -25 - (-10) = -25 + 10 = -15
\][/tex]

2. Use the formula for the [tex]\(n\)[/tex]-th term of an arithmetic sequence:
The general formula for the [tex]\(n\)[/tex]-th term of an arithmetic sequence is:
[tex]\[
a_n = a_1 + (n - 1) \cdot d
\][/tex]
Here, we need to find the 81st term, so [tex]\(n = 81\)[/tex].

3. Substitute the known values into the formula:
- First term ([tex]\(a_1\)[/tex]) = [tex]\(-10\)[/tex]
- Common difference ([tex]\(d\)[/tex]) = [tex]\(-15\)[/tex]
- Term number ([tex]\(n\)[/tex]) = 81

So, we substitute these values into the formula:
[tex]\[
a_{81} = -10 + (81 - 1) \cdot (-15)
\][/tex]

4. Perform the calculations:
- Calculate [tex]\(81 - 1\)[/tex]:
[tex]\[
81 - 1 = 80
\][/tex]
- Multiply this by the common difference [tex]\(d = -15\)[/tex]:
[tex]\[
80 \cdot (-15) = -1200
\][/tex]
- Add this result to the first term [tex]\(a_1 = -10\)[/tex]:
[tex]\[
a_{81} = -10 + (-1200) = -10 - 1200 = -1210
\][/tex]

Therefore, the 81st term of the arithmetic sequence [tex]\(-10, -25, -40, \ldots\)[/tex] is [tex]\(-1210\)[/tex].

Thanks for taking the time to read Find the 81st term of the arithmetic sequence tex 10 25 40 ldots tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada