Arithmetic Progression - Shortcuts & Tricks for Placement Tests, Job Interviews &
Exams
Arithmetic Progression or AP is a crucial concept that appears in most placement
tests or entrance exams. Typically, you will find at least three to four questions
asked from this chapter in a large paper format. In this video, we will learn this
chapter effortlessly and see a lot of variety of questions here.
The nth term that is an is equal to a + (n - 1) x d, where d is the common
difference. This formula is used in almost all the questions of AP, so make sure
that you understand it clearly and remember it.
Another essential formula that I am going to use throughout the chapter that
involves finding the sum of a series that is an AP. Suppose I am given an AP series
whose first term is 'a' and the common difference is 'd'. The series becomes a,
a+d, a+2d, ..., a+(n-1)d. If I try to find the total number of terms in the series,
it is also 'n'. It shows that whatever we have learned till now, we can apply it to
the real-world problems as well.
The formula being referred to here is the formula for the series with 'n' terms in
an Arithmetic Progression (AP).
Instead of just giving you the formula, let's break it down into steps to make it
easier to understand and remember. So, let's take a step further and simplify this
formula:
Sum of 'n' terms = n/2 {2a + (n-1)d}
We can write n/2 as the number of terms divided by 2.
Another important thing to note is that if you add or subtract a certain number
from all the terms of an AP, the resulting series is still in an AP.
Also, for a series to be in an AP, the common difference has to be the same
throughout the series.
Lastly, if you add two AP series together, the resulting series will also be in an
AP. By remembering these important concepts, it will help you solve many questions
directly without needing to do extensive calculations.
The given problem is to find the 15th term of an AP where the ratio of the second
term to the seventh term is 1:3.
Let us denote the first term of the AP as 'a', and the common difference as 'd'.
So, the second term of the AP will be 'a + d' and the seventh term of the AP will
be 'a + 6d'.
Given that (a + d)/(a + 6d) = 1/3.
Solving this equation, we get a = 3d.
Now, we need to find the 15th term of the AP.
The 15th term can be denoted as 'a + 14d'.
Now, we need to find the value of 'a' or 'd' to find the 15th term.
Let's try to find the value of 'd'.
Exams
Arithmetic Progression or AP is a crucial concept that appears in most placement
tests or entrance exams. Typically, you will find at least three to four questions
asked from this chapter in a large paper format. In this video, we will learn this
chapter effortlessly and see a lot of variety of questions here.
The nth term that is an is equal to a + (n - 1) x d, where d is the common
difference. This formula is used in almost all the questions of AP, so make sure
that you understand it clearly and remember it.
Another essential formula that I am going to use throughout the chapter that
involves finding the sum of a series that is an AP. Suppose I am given an AP series
whose first term is 'a' and the common difference is 'd'. The series becomes a,
a+d, a+2d, ..., a+(n-1)d. If I try to find the total number of terms in the series,
it is also 'n'. It shows that whatever we have learned till now, we can apply it to
the real-world problems as well.
The formula being referred to here is the formula for the series with 'n' terms in
an Arithmetic Progression (AP).
Instead of just giving you the formula, let's break it down into steps to make it
easier to understand and remember. So, let's take a step further and simplify this
formula:
Sum of 'n' terms = n/2 {2a + (n-1)d}
We can write n/2 as the number of terms divided by 2.
Another important thing to note is that if you add or subtract a certain number
from all the terms of an AP, the resulting series is still in an AP.
Also, for a series to be in an AP, the common difference has to be the same
throughout the series.
Lastly, if you add two AP series together, the resulting series will also be in an
AP. By remembering these important concepts, it will help you solve many questions
directly without needing to do extensive calculations.
The given problem is to find the 15th term of an AP where the ratio of the second
term to the seventh term is 1:3.
Let us denote the first term of the AP as 'a', and the common difference as 'd'.
So, the second term of the AP will be 'a + d' and the seventh term of the AP will
be 'a + 6d'.
Given that (a + d)/(a + 6d) = 1/3.
Solving this equation, we get a = 3d.
Now, we need to find the 15th term of the AP.
The 15th term can be denoted as 'a + 14d'.
Now, we need to find the value of 'a' or 'd' to find the 15th term.
Let's try to find the value of 'd'.
