Arithmetic Progressions Introduction: You must have observed that in nature, many things follow a certain pattern, such asmthe petals of a sunflower, the holes of a honeycomb, the grains on a maize cob, the spirals on a pineapple and on a pine cone etc.
We now look for some patterns which occur in our day-to-day life. Some such examples are : (i) Reena applied for a job and got selected. She has been offered a job with a starting monthly salary of ` 8000, with an annual increment of Rs. 500 in her salary. Her salary (in `) for the 1st, 2nd, 3rd, . . . years will be, respectively 8000, 8500, 9000, . . . .
(ii) The lengths of the rungs of a ladder decrease uniformly by 2 cm from bottom to top. The bottom rung is 45 cm in length. The lengths (in cm) of the 1st, 2nd, 3rd, . . ., 8th rung from the bottom to the top are, respectively 45, 43, 41, 39, 37, 35, 33, 31
(iii) In a savings scheme, the amount becomes 5/4 times of itself after every 3 years. The maturity amount (in `) of an investment of ` 8000 after 3, 6, 9 and 12 years will be, respectively : 10000, 12500, 15625, 19531.25
(v) Shakila puts Rs.100 into her daughter’s money box when she was one year old and increased the amount by Rs.50 every year. The amounts of money (in `) in the box on the 1st, 2nd, 3rd, 4th, . . . birthday were 100, 150, 200, 250, . . ., respectively.
(vi) A pair of rabbits are too young to produce in their first month. In the second, and every subsequent month, they produce a new pair. Each new pair of rabbits produce a new pair in their second month and in every subsequent month . Assuming no rabbit dies, the number of pairs of rabbits at the start of the 1st, 2nd, 3rd, . . ., 6th month, respectively are : 1, 1, 2, 3, 5, 8
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