Q. 1. Determine k so that k + 2, 4k - 6 and 3k - 2 are three consecutive terms of an AP.
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Q. 2. If m th term of A.P. is , and nth term is , show that the mn th terms is 1.
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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)].
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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.
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Q. 5. Which term of AP: 3, 10, 17 ... will be 84 more than its 13th term?
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Q. 6. If 9th term of an AP is zero, prove that 29th term is double the 19th term.
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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.
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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.
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Q. 10.Find the sum of all odd integers between 78 and 500 which are divisible by 7.
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Q. 11. Find n, if the given value of x is nth term of A.P. 17, 22, 27, 32, ...; x = 267
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Q. 12. Find the sum of all the odd numbers between 100 and 200
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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.
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Q.14. Find the sum 2+4+6+. . . +202
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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?
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Q. 16. 3 times the tenth term is equal to 5 times the twentieth term. Find twentieth term.
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Q. 17.The 5th term of an AP is 24 and its 15th term is 74. Find the sum of its first 10 terms.
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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 – a2) / [2S-(l+a)] .
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Q. 19. If the difference between the 21st and 10th terms of an AP is 55, find the difference between the 45thand 40th terms.
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Q. 20.Find three numbers in an A.P. whose sum is 15 and product 80
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