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This will help Mathematics (Chapter — 5) (A th m P cclass 10) Exercise 5.1 Question 1: In which of the following situations. does the list Of numbers involved make an arithmetic progression, and Why? (i) The taxi fare after each km when the fare is t 15 for the first km and for each additional km. The amount Of air present in a cylinder When a Vacuum pump Of the air remaining in the cylinder at a time. (iii) The cost of digging a well after every metre Of digging, when it costs R150 for the first metre and rises by t50 for each subsequent metre. (iv) The amount Of money in the account every year. When is at compound interest at 8 % annum. Answer 1: (i) Fare for I kmal Fare for 2kmaz = = Fare for a, — c(23+8) - 01 Fare for 4kma, = {(31 + 8) = 09 a, —az = 31 —23 The difference between the successive terms are same. Hence, it is an A.P. (ii) Let. the amount Of air in the x Amount of air left. after first removal X — - x - Amount of air left. after second removal a, — Amount of air left. after third a. 64 16 The difference between the Successive are not Same. Hence. it is not an A.p. (iii) Cost for diuing 1 m deep at = 050 Cost for digging 2 m deep a. t(150 + 50) Qoo Cost for diuing 3 m deep a, = + 50) t250 Cost for digging 4 m deep a. = t(250 50) = BOO a. —a, = 2(K) — 150 = SO a, -az 250 - 200 50 a, -a, = 300-250 = SO The difference between the successive terms are same. Hence, it is an A.P. (iv) Rate = per annum. Principal a, = Amount after 1 year a. u 0000 (1 + Amountafter2years a. u0Boo(1 + = 02597

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