To write the explicit formula for an arithmetic sequence, we need to know the first term \( a_1 \) and the common difference \( d \). The general formula for the \( n \)-th term of an arithmetic sequence is:
\[ a_n = a_1 + (n - 1)d \]
Once we have specific values for \( a_1 \) and \( d \), we can plug them into the formula.
Example Sequence
Let’s say the first term is \( a_1 = 5 \) and the common difference \( d = 3 \).
Substituting into the formula:
\[ a_n = 5 + (n - 1) \cdot 3 \]
Now we can find the 50th term \( a_{50} \):
\[ a_{50} = 5 + (50 - 1) \cdot 3 \] \[ = 5 + 49 \cdot 3 \] \[ = 5 + 147 \] \[ = 152 \]
Now we can also calculate the 59th term \( a_{59} \):
\[ a_{59} = 5 + (59 - 1) \cdot 3 \] \[ = 5 + 58 \cdot 3 \] \[ = 5 + 174 \] \[ = 179 \]
Final Answers
- \( a_n = 5 + (n - 1) \cdot 3 \)
- \( a_{50} = 152 \)
- \( a_{59} = 179 \)
If you have specific values for \( a_1 \) and \( d \) for your arithmetic sequence, please provide them, and I can adjust the calculations accordingly!