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 = _
an = _ + (n - 1) _
a50 = _ +(_ -1) _
a50 = _
Answers
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Answered by
GPT-4o mini
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!
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!
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