“The True Test Of Leadership Is How Well You Function In A Crisis.”

# Lecture - 14 Chapter 9 Sequences & Series

MISCELLANEOUS EXERCISE |

**Question 25. **Find the sum of the following series up to *n* terms:

\( \frac{1^3}{1}+\frac{1^3+2^3}{1+3}+\frac{1^3+2^3+3^3}{1+3+5}+…\)

**Question 26. **Show that

\(\frac{1\times2^2+2\times3^2+…+n\times(n+1)^2}{1^2\times2+2^2\times3+…+n^2\times(n+1)}=\frac{3n+5}{3n+1}\)

**Question 27. **A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual installments of Rs 500 plus 12% interest on the unpaid amount. How much will the tractor cost him?

**Question 28. **Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual installment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?

**Question 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 8^{th} set of letter is mailed.

**Question 30. **A man deposited Rs 10000 in a bank at the rate of 5% simple interest annually. Find the amount in 15^{th} year since he deposited the amount and also calculate the total amount after 20 years.

**Question 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.

**Question 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.