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 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.