- 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]
- Show that if three quantities form any two of the three sequences AS,GS,and HS then they also form the remaining third sequence
- 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.
- Divide 69 in three parts in AP and the product of first two parts is 483
- 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.
- Show that b^2 is greater than, equal to, or less than according as a,b,c are in AP, GP or HP
- If a and b are two positive numbers then prove that AM,GM,HM form GP.
- 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)
- 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)
- 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: \(\frac{32767}{4}\))
- 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)
- 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)

# Exercise

By
Bed Prasad Dhakal
Grade 11
·
Sequence and Series

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