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Arithmetic Progression Class 11 Notes Maths Chapter 9
- If ‘a’ is the first term and ‘d’ is the common difference of the arithmetic progression, then its nth term is given by an = a+(n-1)d
- The sum, Sn of the first ‘n’ terms of the A.P. is given by Sn = n/2 [2a + (n-1)d]
- If Sn is the sum of n terms of an A.P. whose first term is ‘a’ and last term is ‘l’,Sn = (n/2)(a + l)
- If common difference is d, number of terms n and the last term l, then Sn = (n/2)[2l-(n -1)d]
- If a fixed number is added or subtracted from each term of an A.P., then the resulting sequence is also an A.P. and it has the same common difference as that of the original A.P.
- If each term of A.P is multiplied by some constant or divided by a non-zero fixed constant, the resulting sequence is an A.P. again.
- If a1, a2, a3, …, an and b1, b2, b3, …, bn, are in A.P. then a1+b1, a2+b2, a3+b3, ……, an+bn and a1–b1, a2–b2, a3–b3, ……, an–bn will also be in A.P.
- Suppose a1, a2, a3, ……,an are in A.P. then an, an–1, ……, a3, a2, a1 will also be in A.P.
- If nth term of a series is tn = An + B, then the series is in A.P.
- If a1, a2, a3, ……, an are in A.P., then a1 + an = a2 + an–1 = a3 + an–2 = …… and so on.
- In order to assume three terms in A.P. whose sum is given, they should be assumed as a-d, a, a+d.
- Four terms of the A.P. whose sum is given should be assumed as a-3d, a-d, a+d, a+3d
- Five convenient numbers in A.P. a–2b, a–b, a, a+b, a+2 b.
- In general, we take a – rd, a – (r – 1)d, …., a – d, a, a + rd in case we have to take (2r + 1) terms in an A.P.
- Likewise, any 2r terms of an A.P. should be assumed as: a – (2r-1)d, a – (2r – 3)d, …., a – d, a, a + d, ………….. , a+(2r-3)d, a + (2r-1)d.
- The arithmetic mean of two numbers ‘a’ and ‘b’ is (a+b)/2.
- The terms A1, A2, ….. , An are said to be arithmetic means between a and b if a, A1, A2, ….. , An, b is an A.P.
- Clearly, ‘a’ is the first term, ‘b’ is the (n+2)th term and ‘d’ is the common difference. Then, we have b = a+(n+2-1)d = a+(n+1)d
Hence, this gives ‘d’ = (b-a)/(n+1)
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FAQs on Arithmetic Progression Class 11 Notes Maths Chapter 9
| 1. What is an arithmetic progression? |  |
Ans. An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant. For example, 2, 4, 6, 8, 10 is an arithmetic progression with a common difference of 2.
| 2. How do you find the nth term of an arithmetic progression? | |
Ans. The nth term of an arithmetic progression can be found using the formula:
nth term = first term + (n - 1) * common difference
Where the first term is the initial term of the progression, n is the position of the term, and the common difference is the constant difference between any two consecutive terms.
| 3. What is the formula for the sum of an arithmetic progression? | |
Ans. The formula for the sum of an arithmetic progression is:
Sum = (n/2) * (first term + last term)
Where n is the number of terms in the progression, the first term is the initial term, and the last term is the term at the nth position.
| 4. How do you identify an arithmetic progression from a given sequence of numbers? | |
Ans. To identify an arithmetic progression from a given sequence of numbers, you need to check if the difference between any two consecutive terms is constant. If the difference is the same for all pairs of terms, then the sequence is an arithmetic progression.
| 5. Can the common difference in an arithmetic progression be negative? | |
Ans. Yes, the common difference in an arithmetic progression can be negative. In such cases, the terms of the progression will decrease as you move along the sequence. For example, -3, -7, -11, -15 is an arithmetic progression with a common difference of -4.
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