Math 10 CBSE
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❓ 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 ₹ 15 for the first km and ₹ 8 for each additional km.
(ii) The amount of air present in a cylinder when a vacuum pump removes 1/4 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 ₹ 150 for the first metre and rises by ₹ 50 for each subsequent metre. (iv) The amount of money in the account every year, when ₹ 10000 is deposited at compound interest at 8 % per annum.

❓ Write first four terms of the AP, when the first term a and the common difference d are given as follows:
(i) a = 10, d = 10 (ii) a = –2, d = 0
(iii) a = 4, d = – 3 (iv) a = – 1, d = 1/2
(v) a = – 1.25, d = – 0.25

❓ For the following APs, write the first term and the common difference: (i) 3, 1, – 1, – 3, . . .
(ii) – 5, – 1, 3, 7, . . .
(iii) 1/3, 5/3, 9/3, 13/3, ...
(iv) 0.6, 1.7, 2.8, 3.9, . . .

❓ Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.
(i) 2, 4, 8, 16, . . .
(ii) 2, 5/2 , 3, 7/2, ....
(iii) – 1.2, – 3.2, – 5.2, – 7.2, . . .
(iv) – 10, – 6, – 2, 2, . . .
(v) $ 3, 3+\sqrt{2} , 3+2\sqrt{2} , 3+3\sqrt{2} , . . . $
(vi) 0.2, 0.22, 0.222, 0.2222, . . .
(vii) 0, – 4, – 8, –12, . . .
(viii) –1/2, –1/2, –1/2, –1/2, . . .
(ix) 1, 3, 9, 27, . . .
(x) a, 2a, 3a, 4a, . . .
(xi) $ a, a^2, a^3, a^4, . . . $
(xii) $ \sqrt{2}, \sqrt{8}, \sqrt{18} , \sqrt{32}, . . . $
(xiii) $ \sqrt{3},\sqrt{6},\sqrt{9} ,\sqrt{12} , . . . $
(xiv) $ 1^2, 3^2, 5^2, 7^2, . . . $
(xv) $ 1^2, 5^2, 7^2, 73, . . . $
Ans:
mathx_ap_ans_1
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