32. If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation
31. What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?
30. The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2nd hour, 4th hour and nth hour ?
29. If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are
28. The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio
27. Find the value of n so that may be the geometric mean between a and b.
26. Insert two numbers between 3 and 81 so that the resulting sequence is G.P.
25. If a, b, c and d are in G.P. show that
24. Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from
23. If the first and the nth term of a G.P. are a and b, respectively, and if P is the product of n terms, prove that
22. If the terms of a G.P. are a, b and c, respectively. Prove that
2.1 Find four numbers forming a geometric progression in which the third term is greater than the first term by 9, and the second term is greater than the by 18.
20. Show that the products of the corresponding terms of the sequences
form a G.P, and find the common ratio.
19. Find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and 128, 32, 8, 2,1/2
18. Find the sum to n terms of the sequence, 8, 88, 888, 8888… .
17. If the terms of a G.P. are x, y and z, respectively. Prove that x,y, z are in G.P.
16. Find a G.P. for which sum of the first two terms is – 4 and the fifth term is 4 times the third term
15. Given a G.P. with a = 729 and term 64, determine
14. The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P.
13. How many terms of G.P. , … are needed to give the sum 120?