Revision Notes for ICSE Class 10 Math Chapter 10 - Free PDF Download
FAQs on ICSE Class 10 Mathematics Revision Notes Chapter 10 - Arithmetic Progression
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2. What is an Arithmetic Progression?
An arithmetic progression is also known as arithmetic series. It is a sequence of numbers in which the difference between two consecutive numbers is always constant. For example, 5, 6, 7, 8, 9, 10, and so on is an arithmetic progression or arithmetic series with a common difference of 1.
If the initial term of an arithmetic series is a1 and the common difference of consecutive and successive numbers is d, then the nth term of the progression (an) is given by- an= a1+(n-1)d. In general, the formula is an= am+(n-m)d. A finite part of an arithmetic series is known as finite arithmetic progression.
3. What is the method to find the sum of an arithmetic progression?
The sum of numbers or terms in an arithmetic progression is the addition of the first n terms of the AP. The sum is equal to the nth term divided by twice the sum of 2 times of the result of the first term 'a'. And the product of the difference between the first and second term 'd' is also referred to as the common difference between consecutive numbers, and (n-1) where n shows the numbers that need to be added. The formula of the sum of an arithmetic progression is given as-
Sum of n terms in arithmetic progression=n/2[2a+(n-1)d].
4. Write examples of the sum of arithmetic progression?
The examples of the sum of an arithmetic progression are as follows.
1, 4, 9, 16, 25, 36, 49, 64, 81 till 625 shows a sequence or series of squares of natural numbers till 25.
2, 5, 8, 11, 14, 17, 20 forms another series or sequence in which each number proceeds with the addition of the number 3.
If all the terms in a progression proceed with a fixed number except the first number. This progression is known as arithmetic progression. For instance, if a is the first term or number of a finite arithmetic progression and d is a common difference, the progression is written as- a, a+d, a+2d, and so on.
5. Write some important formulas for arithmetic progressions.
The following concepts and formulas are useful to solve problems based on arithmetic progressions.
An arithmetic progression is a list of numbers in which each number is obtained by adding a fixed number to the preceding number.
The first number is represented by a, d is a common difference, n is the number of terms and an is the nth term.
AP is represented as a, a+d, a+2d, and so on.
The nth term is obtained by an= a+(n-1)d.
The sum of an AP is written as sn= n/2[2a+(n-1)d].