Arithmetic progression
The chapter 'Arithmetic progression' is a highly scoring and important topic for the board exams, because it reinforces fundamental concepts and problem-solving skills. It carries 4-6 marks in the examination. It covers concepts like, finding common difference, check whether given sequence is an A.P., problems based on \(n^{th}\) terms and sum of \(n^{th}\) terms.
Most possible variation of question types that we can expect in board exam as per previous year question paper are discussed below.
| Total Marks \(4\) - \(6\) | |
| Variation \(1\) | Variation \(2\) |
Total Mark \(= 6\)
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Total Mark \(= 4\)
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To prepare well for the board examination, it is necessary to understand the following concepts clearly.
- Common differences - based on some common difference or finding common difference
- Checking as an A.P - checking whether given sequence/situation forms an A.P sequence or not
- \(n^{th}\) term of an A.P - finding \(n^{th}\) term and number of terms of an A.P.
- Sum of \(n^{th}\) term of an A.P. - finding the sum of first n terms of an A.P.
| Important Concept (Learning Outcomes) | Expected Question Type | Concept dealt with |
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Sec A -MCQ,
Sec B
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Sec A, Sec C | |
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Sec D, Sec E |
Let us recall the important concpets/formulas involved in Arithmetic progression:
| TO FIND | FORMULAS |
| 1. \(n^{th}\) term | \(a_{n} = a +(n-1)d\) |
| 2. No of terms |
\(n=(\frac{l-a}{d})+1\), \(l= a_{n}\)
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| 3. Common difference | \(d= a_{2}-a_{1} = a_{3}-a_{2} = a_{4}-a_{3}=...\) |
| 4. General term of an AP | \(a, a+d, a+2d, a+3d,...\) \(a_{1}=a , a_{2} = a+d, a_{3}=a+2d, ...\) |
| 5. \(3\) consecutive terms in AP | \(a-d,a,a+d\) |
| 6. \(4\) consecutive terms in AP | \(a-3d,a-d,a+d,a+3d\) |
| 7. Sum of \(n\) terms of an AP | \(S_{n}= \frac{n}{2}(2a+(n-1)d)\) where \(n,d,a\) given |
| 8. Sum of \(n\) terms of an AP | \(S_{n}= \frac{n}{2}(a+l)\) where \(n,l,a\) given |
| 9. \(a_{n}\) if \(s_{n}\) is given |
\(a_{n} = S_{n}-S_{n-1}\)
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