Question
Use your explicit formula to find the 100th term of 2, 7, 12, 17, 22, 27
Answers
Answer
can you use normal numbers
Answered by
GPT-4o mini
The sequence you provided is: 2, 7, 12, 17, 22, 27.
To find the explicit formula, let's first look for a pattern. This sequence is an arithmetic sequence, where each term increases by 5.
- First term (a) = 2
- Common difference (d) = 5
The formula for the \( n \)-th term of an arithmetic sequence is given by:
\[
a_n = a + (n-1) \cdot d
\]
Substituting in the values we have:
\[
a_n = 2 + (n-1) \cdot 5
\]
\[
a_n = 2 + 5n - 5
\]
\[
a_n = 5n - 3
\]
Now, to find the 100th term, we substitute \( n = 100 \) into the formula:
\[
a_{100} = 5(100) - 3
\]
\[
a_{100} = 500 - 3
\]
\[
a_{100} = 497
\]
Thus, the 100th term of the sequence is **497**.
To find the explicit formula, let's first look for a pattern. This sequence is an arithmetic sequence, where each term increases by 5.
- First term (a) = 2
- Common difference (d) = 5
The formula for the \( n \)-th term of an arithmetic sequence is given by:
\[
a_n = a + (n-1) \cdot d
\]
Substituting in the values we have:
\[
a_n = 2 + (n-1) \cdot 5
\]
\[
a_n = 2 + 5n - 5
\]
\[
a_n = 5n - 3
\]
Now, to find the 100th term, we substitute \( n = 100 \) into the formula:
\[
a_{100} = 5(100) - 3
\]
\[
a_{100} = 500 - 3
\]
\[
a_{100} = 497
\]
Thus, the 100th term of the sequence is **497**.
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