For calculating the nth term of an arithmetic progression, use the sequence formula. The arithmetic sequence is the sequence in which the common difference between any two successive terms remains constant. We can use the arithmetic sequence formula to find any term in the arithmetic sequence. Let’s look at some solved examples to better understand the arithmetic sequence formula.

**What Is the Sequence Formula?**

An arithmetic sequence is composed of the following terms: a, a +d, a+2d, a+3d, The first term is a the common difference is d, and n represents the number of terms. Identify the AP and find the first term, several terms, and common differences for the calculation using the arithmetic sequence formulas.

### The formula for Arithmetic Sequence

The sequence formula is as follows:

Formula 1 is the sequence formula.

an=a1+(n1) d where an is the nth term, a1 is the first term, and d is the common difference

Formula 2: The sum of the first n terms in an arithmetic sequence is given as,

Sn=n2[2a+(n−1) d]

where Sn is the sum of n terms, a1 is the first term, and d is the common difference between the successive terms

Formula 3: The formula for calculating an AP’s common difference is d=anan1 where an is the nth term, an1 is the second last term, and d is the common difference between the successive terms.

**Applications of Arithmetic Sequence Formula**

Every day, if not every minute, we use the arithmetic sequence formula without even realizing it. Here are a few examples of real-world applications of the sequence formula.

An arithmetic sequence is used to arrange seats in a stadium or auditorium.

The second hand on the clock, like the minutes and hour hands, moves in Sequence.

The weeks in a month, as well as the years, follow the AP.

Every year, the number of candles blown on a birthday grows in a sequence.

##### Examples Using Sequence Formula

Example 1: Using the sequence formula, find the 13th term in the sequence 1, 5, 9, and 13…

Solution: Find the 13th term in the given sequence.

Because the difference between consecutive terms is the same, the given sequence is a sequence.

a = 1, d = 4

Using the sequence formula, an=a1+(n1)d

For the 13th term, n = 13 a = 1 + (13 – 1)

4 a = 1 + (12)

4 a = 1 + 48 \ an = 49

**Answer: 13**^{th }**term in the sequence is 49.**

Example 2: Determine the first term in a sequence in which the 35th term is 687 and the common difference is 14.

To find: the first term in the sequence Given: a = nth term, d = 14

Applying the Sequence Formula

an=a1+(n−1)

d 687 = a1 + (35 – 1)

14 687 = a1 + (34)

14 687 = a1 + 476 \sa1 = 211

**The first number in the sequence is 211.**

**FAQs on Sequence Formula**

**What Does the Algebraic Sequence Formula Mean?**

The term ” sequence formula” refers to the formula used to calculate a sequence’s general term and the sum of its n terms.

**What Is n in Sequence Formula?**

The number of terms in the given sequence is indicated by the symbol n in the formula for finding the general term in a sequence, an=a1+(n1)d.

**. What is the formula for the sum of n terms in a sequence?**

The formula for the sum of the first n terms in a sequence is Sn=n2[2a+(n1)d], where Sn stands for the sum of the first n terms, a1 for the first term, and d for the common difference.