1st Year Math Notes Chapter 6

• Our comprehensive 1st Year Math Notes Chapter 6 will ensure you're fully prepared for your exams.
• Definition of sequence with examples
• Definition of a real sequence with examples
• Definition of a finite and infinite sequence with examples.
• Examples and Exercises Solutions of complete Chapter.
  
• Definition of arithmetic progression with examples
  
• Definition of geometric progression with examples
• Definition of Arithmetic Mean with examples
• Definition of geometric mean with examples
• Definition of vulgar fraction and a proper fraction
• Definition of harmonic progression with examples
• Definition of harmonic mean with examples
• Relation between A.M, G.M, and H.M
• Prove that arithmetic < geometric < harmonic
• What is the Sigma notation or summation notation
• Arithmetic Mean (A.M): A number A is said to be the A.M. between the two numbers a and b if a, A, b are in A.P. If d is the common diference of this A.P., then A - a = d and b - A = d.
• Note: Middle term of three consecutive terms in A.P. is the A.M. between the extreme terms.
• Series: The sum of an indicated number of terms in a sequence is called a series. For example, the sum of the irst seven terms of the sequence {n2} is the series, 1 + 4 + 9 + 16 + 25 + 36 + 49. The above series is also named as the 7th partial sum of the sequence {n2}. If the number of terms in a series is inite, then the series is called a inite series, while a series consisting of an unlimited number of terms is termed as an ininite series. Sum of irst n terms of an arithmetic series:
• The sum of three numbers in an A.P. is 24 and their product is 440. Find the numbers.
• Find four numbers in A.P. whose sum is 32 and the sum of whose squares is 276.
• Find the ive numbers in A.P. whose sum is 25 and the sum of whose squares is 135.
• The sum of the 6th and 8th terms of an A.P. is 40 and the product of 4th and 7th term is 220. Find the A.P. 
• Word Problems on A.p: Example 1: Tickets for a certain show were printed bearing numbers from 1 to 100. Odd number tickets were sold by receiving paisas equal to thrice of the number on the ticket while even number tickets were issued by receiving paisas equal to twice of the number on the ticket. How much amount was received by the issuing agency?
• A man deposits in a bank Rs. 10 in the irst month; Rs. 15 in the second month; Rs. 20 in the third month and so on. Find how much he will have deposited in the bank by the 9th month.
• 378 trees are planted in rows in the shape of an isosceles triangle, the numbers in successive rows decreasing by one from the base to the top. How many trees are there in the row which forms the base of the triangle?
• A man borrows Rs. 1100 and agree to repay with a total interest of Rs. 230 in 14 installments, each installment being less than the preceding by Rs. 10. What should be his irst installment?
• A clock strikes once when its hour hand is at one, twice when it is at two and so on. How many times does the clock strike in twelve hours ?
• A student saves Rs.12 at the end of the irst week and goes on increasing his saving Rs.4 weekly. After how many weeks will he be able to save Rs.2100?