# Exercise

1. Integration to Investment and Growth: Determine the monthly repayments needed to repay a 100000 loan which is paid back over 25 years when the interest rate is 8% compounded annually[Ans: 780.66]
2. Show that if three quantities form any two of the three sequences AS,GS,and HS then they also form the remaining third sequence
3. The sum of three numbers in AP is 36. When the numbers are increased by 1,4,43 respectively, the resulting numbers are in GP, find the numbers.
4. Divide 69 in three parts in AP and the product of first two parts is 483
5. If a be the AM between b and c, b be the GM between c and a, then prove that c will be HM between a and b.
6. Show that b^2 is greater than, equal to, or less than according as a,b,c are in AP, GP or HP
7. If a and b are two positive numbers then prove that AM,GM,HM form GP.
8. If the $4^{th}$ and $15^{th}$ terms of an arithmetic series are 11 and 44 respectively then, find the sum of its first 20 terms. (Ans:610)
9. Puja gets an employment of Rs.25000 in a month with an annual increment of Rs. 1500. How much does she earn in six years? Find her salary at 12^{th} year. (Ans: Rs.190500, Rs.41500)
10. In a geometric series, if the sixth term is 16 times the second term and the sum of first seven terms is $\frac{127}{4}$ , then find the sum of the first 15 term. (Ans: $\frac{32767}{4}$)
11. There are 8 bags full of books. The numbers of books in each bag form a GP. If the $4^{th}$ and $6^{th}$ bags contain 24 and 96 books respectively, find the number of the books in the $1^{th}$ and last bags. ( Ans: 3, 384)
12. One side fo a square is 10 cm . The mid point of its sides are joined to form another square, whose mid point are again joined t form one more square. The process is continued indefinitely. Find the sum of the areas of all the squares so formed. (Ans:200 square cm)