A sequence is a set of numbers in a particular order or a set of numbers that follow a pattern. The most basic sequential order example is that of counting numbers 1, 2, 3, 4 and so on. The numbers follow an increasing pattern (1, 2, 3…). These numbers don’t necessarily have to be continuous to be a sequence. Let’s take an example of a sequential order question that has an increment of two, like 1 3 5. There are just two things you need to know about any sequence: first, how do you find the nth term of a sequence and second how do you define the sequence.

Finding the nth term means, say, I asked you the 31st term of the sequence, and you have no time to write all the 31 terms to find out that we need to have a formula.

Formula:

1st+ (n-1) d

The first term plus, n minus 1 time D. If we want to find the 31st term, we just substitute 31 in place of n while D is the difference between any two continuous terms. It’s called the common difference.

**Sequences**

There are 2 types of progressions that we see and use: Arithmetic and Geometric. These examples are for arithmetic progression.

**Some common examples of sequential order questions are**

Ex1- The sequence a is defined using this formula: An= 4n+1. Find the common difference.

Solution1- Common difference D is equal to 4. In an arithmetic sequence, the coefficient of n is a common difference, n is the term number. Another way in which we can find the common difference is by finding the first few terms. The first term will be a 1; the first term of this sequence is 5. Similarly, the second term will be 9, and the third term will be 13the sequence will be 5 9 13 and so on. And you can see that the common difference is 4, but this method would be too time-consuming.

**Another Example of a sequential order question**

Ex2- The first few terms of the sequence (2,6,10…). Find the 17th term.

Solution 2- This is an arithmetic term as the difference between two continuous terms is constant, and we know that the nth term of an arithmetic sequence is given by the formula a plus n minus 1 time D. a is the first term, n is the term number and D is a common difference. So, finding the 17th term will be pretty easy. Here the first term is 2, as the term number is 17. So, we write this as:

17th term= 2+(17-1) *3

This is one of the most asked around the example of sequential order questions:

Ex3- An auditorium has ten seats in the first row, 14 in the second, 18 in the third, and so on. The auditorium has a total of 18 rows. How many seats are there in total?

Solution 3- The sum of an AP is n over 2 multiplied by the sum of the first and last term. n will be the last term number, a – the first term number, i.e., 10

Sum=n/2(FT+LT)

FT=A=10

Nth term=a+(n-1) d

LT=10+(18-1)4

=10+68= 78

Sum= 18/2(10+78)

=792 ANS

**Here’s another interesting sequential order example**

Exp4- The sequence is 4n, and the 16th term of this sequence is 4,294,967,192. Is this true or false?

Solution 4- The first term is 4 raised to 1 that equals 4, the second term is 4 raised to 2 that equals 16, the third term is 4 raised to 3 that equals, the fourth term is 4 raised to 4= 256. Look at the unit digits of every term. It’s either 4 or 6. So definitely false.

**Conclusion**

These were just the fundamental examples of sequential order in AP; there are various types of questions on the same concept but with different difficulties and advancements. These examples just provided you with the basic framework for how you should approach the questions. There are a lot more questions that need to be gone through. Not only AP but GP is also an interesting topic, and if you are studying AP, it is highly recommended to go for GP as well.