32. 150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second day, 4 more workers dropped out on third day and so on.
31. A manufacturer reckons that the value of a machine, which costs him Rs. 15625, will depreciate each year by 20%. Find the estimated value at the end of 5 years.
30. A man deposited Rs 10000 in a bank at the rate of 5% simple interest annually. Find the amount in 15th year since he deposited the amount and also calculate the total amount after 20 years.
29. A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage when 8th set of letter is mailed.
28. Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?
27. A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much will the tractor cost him?
26. Show that
25. Find the sum of the following series up to n terms:
24. If are the sum of first n natural numbers, their squares and their cubes, respectively, show that
23. Find the sum of the first n terms of the series: 3+ 7 +13 +21 +31 +…
22. Find the 20th term of the series terms.
21(ii) Find the sum of the following series up to n terms:
.6 +. 66 +. 666+…
21(i) Find the sum of the following series up to n terms:
20. If a, b, c are in A.P.; b, c, d are in G.P. and 1/c , 1/d , 1/e are in A.P. prove that a, c, e are in G.P.
19. The ratio of the A.M. and G.M. of two positive numbers a and b, is m : n. Show that
18. If a and b are the roots of and c, d are roots of , where a, b, c, d form a G.P. Prove that (q + p) : (q – p) = 17:15.
17. If a, b, c, d are in G.P, prove that are in G.P.
16. If are in A.P., prove that a, b, c are in A.P.
15. The pth, qth and rth terms of an A.P. are a, b, c, respectively. Show that
14. Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that