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A.P. & G.P. Section- 1

1.If a, b, c are in G.P., then the equations ax² + 2bx + c = 0 and dx² + 2ex + f = 0 have a common root if d/a, e/b, f/c are in






2. If a, b, c are in AP then






3.Three numbers form an increasing GP. If the middle term is doubled, then the new numbers are in Ap. The common ratio of GP is






4.The sum of n terms of the series (1/1.2) + (1/2.3) + (1/3.4) + …… is






5. If 1/(b + c), 1/(c + a), 1/(a + b) are in AP then






6.The sum of series 1/2! + 1/4! + 1/6! + ….. is






7. The third term of a geometric progression is 4. The product of the first five terms is






8.Let Tr be the r th term of an A.P., for r = 1, 2, 3, … If for some positive integers m, n, we have Tm = 1/n and Tn = 1/m, then Tm n equals






9.The sum of two numbers is 13/6 An even number of arithmetic means are being inserted between them and their sum exceeds their number by 1. Then the number of means inserted is






10.If the sum of the roots of the quadratic equation ax² + bx + c = 0 is equal to the sum of the squares of their reciprocals, then a/c, b/a, c/b are in






11.If 1/(b + c), 1/(c + a), 1/(a + b) are in AP then






12. The 35th partial sum of the arithmetic sequence with terms an = n/2 + 1






13. The sum of two numbers is 13/6 An even number of arithmetic means are being inserted between them and their sum exceeds their number by 1. Then the number of means inserted is






14.The first term of a GP is 1. The sum of the third term and fifth term is 90. The common ratio of GP is






15. The sum of AP 2, 5, 8, …..up to 50 terms is






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