Question

Write an explicit formula ((an = a1 + (n - 1)d) for the given arithmetic sequence. Use your explicit formula to find the 50th term of the sequence

an = _ + (n - 1) _

a50 = _ +(_ -1) _

a50 = _

Answer 1

To write the explicit formula for an arithmetic sequence, you need the first term \( a_1 \) and the common difference \( d \).

The general explicit formula for the \( n \)-th term of an arithmetic sequence is given by:

\[
a_n = a_1 + (n - 1)d
\]

### Step 1: Determine \( a_1 \) and \( d \)

If you provide the first term \( a_1 \) and the common difference \( d \) of the arithmetic sequence, I can fill in the blanks and calculate the 50th term.

For example, if the first term \( a_1 = 3 \) and the common difference \( d = 2 \):

\[
a_n = 3 + (n - 1) \cdot 2
\]

### Step 2: Find the 50th term

Using \( n = 50 \):

\[
a_{50} = 3 + (50 - 1) \cdot 2
\]

Calculating it:

\[
a_{50} = 3 + 49 \cdot 2
\]
\[
a_{50} = 3 + 98
\]
\[
a_{50} = 101
\]

Please provide the values for the first term and the common difference to proceed with your specific sequence!