What is the arithmetic sequence formula?
Arithmetic sequence is the most common type of sequence used in Mathematics. It is compulsory for every student to learn about this particular sequence type. No doubt, you can solve a problem related to it using the general arithmetic sequence formula.
But it can be difficult when you have to rearrange the formula for finding a specific term of the sequence. For example, you can find the nth term using the general formula but you have to rearrange the formula for calculating the first term.
It will be hard for you to do so and get a new form of the arithmetic sequence formula. That's why, we have written this blog to help you understand other forms of that formula. You should read this blog till the end to memorize other forms of this particular formula.
What is the Explicit formula for the arithmetic sequence?
Before learning the explicit formula for an arithmetic sequence, you should understand what the term “explicit” means. It is a general word that means “direct&rdquo.In terms of an arithmetic sequence, the explicit formula is a specific formula that explains the entire sequence.
It means that we don’t need to write the other terms of the sequence to understand it. If we know the explicit formula for an arithmetic sequence, we can understand the entire sequence using basic mathematical knowledge.
Here is the explicit formula for the arithmetic sequence.
an = a + (n - 1)d
We can convert this formula into the explicit formula by inserting the value of “a” and “d”.
What is the Recursive formula for an arithmetic sequence?
The recursive formula for an arithmetic sequence is a particular form of the formula using which we can find the next term of the sequence with the help of previous ones. It means that this formula type is a dependent form of the formula.
For example, if you are given the 8th term of the sequence and common difference, you can find the 9th term of the arithmetic sequence using this formula. It is not possible in a simple way through the general formula of an arithmetic sequence.
Here is the simplest form of recursive formula for an arithmetic sequence.
an + 1 = an + d
What is the sum formula for the arithmetic sequence?
It is right to say that the sum formula for an arithmetic sequence is the least used formula related to this term. The reason is general questions involve only the calculation of the nth term of the missing term of the sequence.
But you still need to understand this formula to solve problems related to it. The sum formula for the arithmetic sequence is a particular way to calculate the sum of all terms of the sequence without adding them manually.
Here is the general form of this particular formula related to the arithmetic sequence.
Sum of Arithmetic Sequence Formula = n/2 (a + L)
This formula is used when the last term of the sequence is given. Here, “a” is the first term, “n” is the number of terms, and “L” is the last term of the sequence. If the last term of the sequence is not given, the sum formula for the arithmetic sequence will be written as,
Sum of Arithmetic Sequence Formula = n/2 {2a +(n - 1)d}
Using this formula, you can find the sum of any arithmetic sequence even if you don’t know the last term of the sequence.
What is the Nth term formula for the arithmetic sequence?
The most common formula for an arithmetic sequence is this one in which we can find the nth term of the sequence. Using this arithmetic sequence formula nth term, we can find any term of this particular sequence.
We only need a common difference, the number of terms to be found, and the first term of the sequence. Here is the general formula related to the calculation of the nth term,
an = a + (n - 1)d
Conclusion
In the above sections, we have shared different forms of the arithmetic sequence formula. You may have learned about these formulas in detail from this page.
If you want to learn more about them or have a clear demonstration of the solution, you can use the Arithmetic Sequence Calculator. This online resource will help you in solving problems related to this sequence and enable you to understand the solution deeply with a clear explanation.
FAQ
How do you find the formula for an arithmetic sequence?
The formula for finding the nth term in an arithmetic sequence is given below:
an = a + (n - 1)d
How do I use the explicit formula to find a term in an arithmetic sequence?
The explicit formula for an arithmetic sequence is written by writing the first term of and the common difference in the general formula. By using the number of concerned terms in the sequence, we can find its value.
What is the recursive formula for 2, 4, 7, and 11?
The general recursive formula for this sequence can be written as,
an = an-1 + n
What are some applications of an arithmetic sequence?
An arithmetic sequence is used widely in real-life problems like,
- It helps in stacking cards, chairs, and bowls in a pattern.
- Using this approach, the number of seats in places like stadiums is labeled.
- Arithmetic sequence has been used in the movement of the second hand of a clock.
What is the arithmetic series formula?
The arithmetic series formula is given by,
Sn = n/2 {2a +(n - 1)d}
What is the sum of the expression 1, 2, 3, 4, 5, 6, 7, up to 100 terms?
The sum of the given expression will be 5050.
How do you find the nth number in an arithmetic sequence?
We can find the nth term of the arithmetic sequence using the following formula:
an = a + (n - 1)d
