The sequence 5, 8, 11, 14, 17, 20 is arithmetic because you are adding 3 each time.
The fifth term of the sequence using subscript notation is \( a_5 = 17 \).
Now, let's write the explicit formula for the arithmetic sequence. The first term \( A_1 = 5 \) and the common difference \( D = 3 \). The explicit formula is:
\[ a_n = A_1 + (n-1)D = 5 + (n-1) \cdot 3 \]
To find the 50th term, we substitute \( n = 50 \) into the formula:
\[ a_{50} = 5 + (50 - 1) \cdot 3 \] \[ a_{50} = 5 + 49 \cdot 3 \] \[ a_{50} = 5 + 147 \] \[ a_{50} = 152 \]
So, the answers are:
- \( a_5 = 17 \)
- \( a_n = 5 + (n-1) \cdot 3 \)
- \( a_{50} = 152 \)