Question

Find the 55th term of the arithmetic sequence minus, 7, comma, minus, 5, comma, minus, 3, comma, dot dot dot−7,−5,−3,...

Answer 1

To find the 55th term of the arithmetic sequence given by \(-7, -5, -3, \ldots\), we first need to identify the first term and the common difference of the sequence.

1. **Identify the first term**:
The first term \( a \) is:
\[
a = -7
\]

2. **Determine the common difference**:
The common difference \( d \) can be calculated by subtracting the first term from the second term:
\[
d = -5 - (-7) = -5 + 7 = 2
\]

3. **Use the formula for the \( n \)-th term of an arithmetic sequence**:
The formula for the \( n \)-th term \( a_n \) of an arithmetic sequence is given by:
\[
a_n = a + (n - 1) \cdot d
\]
where \( a \) is the first term, \( d \) is the common difference, and \( n \) is the term number.

4. **Substitute values to find the 55th term**:
We need to find \( a_{55} \):
\[
a_{55} = -7 + (55 - 1) \cdot 2
\]
Now simplifying this, we first calculate \( 55 - 1 = 54 \):
\[
a_{55} = -7 + 54 \cdot 2
\]
Next, calculate \( 54 \cdot 2 = 108 \):
\[
a_{55} = -7 + 108
\]
Finally, calculate:
\[
a_{55} = 101
\]

Thus, the 55th term of the arithmetic sequence is:
\[
\boxed{101}
\]