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

Answer 1

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:

\[ a_{110} = 330 \]