To write an explicit formula for an arithmetic sequence, we need two pieces of information: the first term \( a_1 \) and the common difference \( d \).
Let's denote the first term as \( a_1 \) and the common difference as \( d \). The explicit formula for the nth term of the arithmetic sequence is given by:
\[ a_n = a_1 + (n - 1)d \]
Now, you mentioned you want to find the 50th term \( a_{50} \) of the sequence. The formula for \( a_{50} \) can be plugged into the explicit formula:
\[ a_{50} = a_1 + (50 - 1)d = a_1 + 49d \]
You'll need to provide the values of \( a_1 \) and \( d \) to complete this formula and find \( a_{50} \).
Assuming you have example values, let's say:
- \( a_1 = 3 \) (the first term)
- \( d = 2 \) (the common difference)
The explicit formula would be:
\[ a_n = 3 + (n - 1) \times 2 \]
Now, we calculate \( a_{50} \):
\[ a_{50} = 3 + (50 - 1) \times 2 \] \[ a_{50} = 3 + 49 \times 2 \] \[ a_{50} = 3 + 98 \] \[ a_{50} = 101 \]
Finally, here is the explicit formula and the 50th term filled in:
Explicit Formula: \[ a_n = 3 + (n - 1) \cdot 2 \]
Finding the 50th Term: \[ a_{50} = 3 + (50 - 1) \cdot 2 = 3 + 49 \cdot 2 = 101 \]
If you provide specific values for \( a_1 \) and \( d \), I can give the explicit formula and the 50th term with those numbers.
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