Question

Find the 68th term of the arithmetic sequence minus, 19, comma, minus, 33, comma, minus, 47, comma, dot dot dot−19,−33,−47,...

Answer 1

To find the 68th term of the arithmetic sequence \(-19, -33, -47, \ldots\), we first need to identify the first term and the common difference of the sequence.

1. **Identify the first term (a)**:
The first term, \(a\), is \(-19\).

2. **Identify the common difference (d)**:
We can calculate the common difference \(d\) by subtracting the first term from the second term:
\[
d = -33 - (-19) = -33 + 19 = -14
\]

3. **Use the formula for the nth term of an arithmetic sequence**:
The formula for finding the \(n\)th term 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. **Calculate the 68th term (\(a_{68}\))**:
Plug \(n = 68\), \(a = -19\), and \(d = -14\) into the formula:
\[
a_{68} = -19 + (68-1) \cdot (-14)
\]
Simplifying inside the parentheses:
\[
a_{68} = -19 + 67 \cdot (-14)
\]
Calculating \(67 \cdot (-14)\):
\[
67 \cdot -14 = -938
\]
Now substitute this back into the equation:
\[
a_{68} = -19 - 938
\]
Combine the terms:
\[
a_{68} = -957
\]

Therefore, the 68th term of the arithmetic sequence is \(\boxed{-957}\).