## Arithmetic Progressions questions

**A list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term is called Arithmetic Progressions. This fixed number is called the common difference of the AP .**

**The common difference is denoted by d and the first term by a.**

**Then the AP beco mes: a, a + d a + 2d, a + 3d, . . .,**

**T1 = a ; T2 = a+ d ; T3 = a +2d ; T4 = a + 3d ……….Tn = a + (n-1)d**

**So, the nth term an of the AP with first term a and common difference d is given by an = a + (n – 1) d.**

**So, T2 – T1 = T3 – T2 = . . . = an – a(n – 1) = d.**

**an is also called the general term of the AP.**

**If there are m terms in the AP, then am represents the last term which is sometimes also denoted by l**

**Arithmetic Progressions having finite number of terms is called a finite AP.Eg. The heights ( in cm ) of some students of a school standing in a queue in the morning assembly are 147 , 148, 149, . . ., 157.**

**Arithmetic Progressions having (APs) has finite number of terms is called infinite Arithmetic Progressions. Such APs do not have a last term.**

**Eg. The minimum temperatures ( in degree celsius ) recorded for a week in the month of January in a city, arranged in ascending order are – 3.1, – 3.0, – 2.9, – 2.8, – 2.7, – 2.6, – 2.5**

**Q. 1. Determine k so that k + 2, 4k - 6 and 3k - 2 are three consecutive terms of an AP.**

**Q. 2. If m th term of A.P. is , and nth term is , show that the mn th terms is 1.**

**Q. 3. The first, second and the last terms of an AP are p, q and 2p respectively. Show that its sum is [3pq]/[2(q-p)].**

**Q. 4. A circle is completely divided into n sectors in such a way that the angles of the sectors are in arithmetic progression. If the smallest-of these angles is 8° and the largest 72°, calculate n and the angle in the fourth sector.**

**Q. 5. Which term of AP: 3, 10, 17 ... will be 84 more than its 13th term?**

**Q. 6. If 9th term of an AP is zero, prove that 29th term is double the 19th term.**

**Q. 7. Find a, b such that 27, a, b - 6 are in A.P.**

**Q. 8. For what value of n, the nth terms of the sequences 3, 10, 17,... and 63, 65, 67,... are equal.**

**Q. 9. If m times the m th term of an AP is equal to n times its nth term show that the (m + n)th term of the AP is zero.**

**Q. 10.Find the sum of all odd integers between 78 and 500 which are divisible by 7.**

**Q. 11. Find n, if the given value of x is nth term of A.P. 17, 22, 27, 32, ...; x = 267**

**Q. 12. Find the sum of all the odd numbers between 100 and 200**

**Q. 13.If 10 times the 10th term of an AP is equal to 15 times its 15th term, show that its 25th term is zero.**

**Q.14. Find the sum 2+4+6+. . . +202**

**Q. 15. How many terms are there in the A.P -1,-5/6,-2/3,-1/2……….10/3? Also find its general term?**

**Q. 16. 3 times the tenth term is equal to 5 times the twentieth term. Find twentieth term.**

**Q. 17.The 5th term of an AP is 24 and its 15th term is 74. Find the sum of its first 10 terms.**

**Q. 18. If the first term and last term of an AP are a and l respectively and its sum is S , prove that the common difference of the AP is equal to (l2 – a 2 ) / [2S-(l+a)] .**

**Q. 19. If the difference between the 21st and 10th terms of an AP is 55, find the difference between the 45thand 40th terms.**

**Q. 20.Find three numbers in an A.P. whose sum is 15 and product 80**

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Sample paper 1

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Sample paper 3

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Circle (Important Question)

**Arithmetic Progression**

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