What is the value of the arithmetic series S4?
Understand the Problem
The question is asking for the value of the fourth term in an arithmetic series. This requires knowing the first term and the common difference of the series to find S4, which typically represents the sum of the first four terms.
Answer
$ a_4 = a_1 + 3d $
Answer for screen readers
The value of the fourth term in the arithmetic series is given by the formula $a_4 = a_1 + 3d$.
Steps to Solve
- Identify the First Term and the Common Difference
Let's denote the first term of the arithmetic series as $a_1$ and the common difference as $d$. The values of $a_1$ and $d$ need to be known to proceed.
- Write the Formula for the nth Term
The formula for the nth term of an arithmetic series is given by:
$$ a_n = a_1 + (n - 1)d $$
Here, $n$ is the term number we want to find. For the fourth term, substitute $n = 4$ into the formula.
- Substitute the Values into the Formula
Once we have $a_1$ and $d$, substitute these values into the equation for the fourth term:
$$ a_4 = a_1 + (4 - 1)d $$
This simplifies to:
$$ a_4 = a_1 + 3d $$
- Calculate the Fourth Term
Now, compute the value of $a_4$ using the specific values for $a_1$ and $d$.
The value of the fourth term in the arithmetic series is given by the formula $a_4 = a_1 + 3d$.
More Information
The fourth term in an arithmetic sequence is simply determined by the first term and the common difference. Each term is spaced evenly by the common difference, making it straightforward to find any term if the first term and the difference are known.
Tips
- Neglecting to properly identify the first term and common difference can lead to errors in calculating the fourth term.
- Mistaking $d$ as the first term instead of the common difference.
