STAY ABOVE THE REST 1. If there are (2n+1) terms in AP, then prove that the ratio of the sum of odd terms and the sum of even terms is (n+1):n 2. The ratio of the sums of m and n terms of an AP is m2:n2. Show that the ratio of mth and nth terms is (2m-1) : (2n-1) 3. If pth and rth terms of an AP are a,b,c respectively, then show that:- (i) a(q - r) + b(r - p) + c (p - q) = 0 (ii) (a - b)r + (b - c)p + (c - a)q = 0 4. If (m + 1)th term of an AP is twice the (n+1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term. 5. If an AP consists of n terms with first term an and nth term l. Show that the sum of the mth term form the beginning and the mth term form then end is (a + l) 6. Find 4 no’s in AP whose sum is 20 and the sum of whose squares is 120. 7. Divide 32 into four parts which are in AP such that the product of extremes is to the product of means is 7:15 8. If the numbers a ,b, c, d, e form an AP the find the value of a- 4b + 6c – 4d +e 9. If an+1 + bn+1 is the AM b/w a and b. then find the value of n an + bn 10. Show that (a - b)2, (a2 + b2) and (a + b)2 are in AP 11. The digits of positive integer, having there digits are in AP and their sum is 15. the number obtained by reversing the digits is 594 less than the original number. Find the number. 12. Tow cars starts together in the same direction from the same place. . The first goes with uniform speed of 10km/hr. The second gors at a speed of 8km/hr in the first hour and increases the speed by ½ km in succeeding hours. After how many hours will the second car overtake the first car if both cars go non stop? 13. If a1, a2, a3…an are in AP of non zero terms prove that 1 + 1 … + 1 = n-1 a1a2 a2a3 anan a1an
Posted on: Tue, 05 Nov 2013 12:16:49 +0000
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