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Question content area topPart 1Find the 110th term of the following sequence.3 comma 6 comma 9 comma ...Question content area bottomPart 1a 110equalsenter your response here
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GPT-4o mini
The given sequence is \(3, 6, 9, \ldots\). This is an arithmetic sequence where the first term \(a = 3\) and the common difference \(d = 3\).
The formula for the \(n\)-th term of an arithmetic sequence is given by:
\[
a_n = a + (n - 1) \cdot d
\]
To find the 110th term (\(a_{110}\)), we can substitute \(n = 110\), \(a = 3\), and \(d = 3\) into the formula:
\[
a_{110} = 3 + (110 - 1) \cdot 3
\]
Calculating this step-by-step:
1. Calculate \(110 - 1\):
\[
110 - 1 = 109
\]
2. Multiply \(109\) by \(3\):
\[
109 \cdot 3 = 327
\]
3. Add \(3\) to \(327\):
\[
a_{110} = 3 + 327 = 330
\]
Thus, the 110th term of the sequence is:
\[
a_{110} = 330
\]
The formula for the \(n\)-th term of an arithmetic sequence is given by:
\[
a_n = a + (n - 1) \cdot d
\]
To find the 110th term (\(a_{110}\)), we can substitute \(n = 110\), \(a = 3\), and \(d = 3\) into the formula:
\[
a_{110} = 3 + (110 - 1) \cdot 3
\]
Calculating this step-by-step:
1. Calculate \(110 - 1\):
\[
110 - 1 = 109
\]
2. Multiply \(109\) by \(3\):
\[
109 \cdot 3 = 327
\]
3. Add \(3\) to \(327\):
\[
a_{110} = 3 + 327 = 330
\]
Thus, the 110th term of the sequence is:
\[
a_{110} = 330
\]
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