Question
14. The rule for a sequence is \( a_{n}=n^{2}-n \). The first three terms are 0,2 , and 6 . What is the tenth term?
Ask by Griffin Powers. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The tenth term is 90.
Solution
1. The rule for the sequence is given by
\[
a_{n} = n^2 - n.
\]
2. To find the tenth term, substitute \( n = 10 \) into the formula:
\[
a_{10} = 10^2 - 10.
\]
3. Compute \( 10^2 \):
\[
10^2 = 100.
\]
4. Now subtract 10:
\[
a_{10} = 100 - 10 = 90.
\]
Thus, the tenth term of the sequence is \( 90 \).
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Simplify this solution Mind Expander
To find the tenth term of the sequence defined by \( a_{n} = n^{2} - n \), we can substitute \( n = 10 \) into the formula: \[ a_{10} = 10^{2} - 10 = 100 - 10 = 90 \] So, the tenth term is 90! Now, isn't it cool how sequences can reveal patterns? If you observe the pattern of the sequence a bit more closely, you'll see that it's a quadratic function, which means it’s got a parabolic shape when you graph the terms. This can give you clues about how the numbers will grow as n increases – quite handy for predicting future terms without calculating each one!
