The first term in an arithmetic sequence is -5 and the second term is -3. what is the 50th term? (Recall that in an arithmetic sequence, the difference between successive terms is constant).

Answer

To find the 50th term of the arithmetic sequence where the first term \( a_1 = -5 \) and the second term \( a_2 = -3 \), we can follow these steps:

### Step 1: Identify the first term and the second term
The first term \( a_1 \) is given as:
\[ a_1 = -5 \]
The second term \( a_2 \) is given as:
\[ a_2 = -3 \]

### Step 2: Calculate the common difference \( d \)
The common difference \( d \) in an arithmetic sequence is calculated as:
\[ d = a_2 - a_1 \]
Substituting the values we have:
\[ d = -3 - (-5) = -3 + 5 = 2 \]

### Step 3: Use the formula for the nth term
The formula for the nth term \( a_n \) of an arithmetic sequence is:
\[ a_n = a_1 + (n - 1) \cdot d \]
We need to find the 50th term, so we set \( n = 50 \):
\[ a_{50} = a_1 + (50 - 1) \cdot d \]

### Step 4: Substitute the values into the formula
Now we substitute \( a_1 = -5 \), \( d = 2 \), and \( n = 50 \):
\[ a_{50} = -5 + (50 - 1) \cdot 2 \]
This simplifies to:
\[ a_{50} = -5 + 49 \cdot 2 \]

### Step 5: Calculate the value
Now we calculate \( 49 \cdot 2 \):
\[ 49 \cdot 2 = 98 \]
So we have:
\[ a_{50} = -5 + 98 = 93 \]

### Final Answer
Thus, the 50th term of the arithmetic sequence is:
\[ \boxed{93} \]

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