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(i) 3, 1, –1, –3 …

(ii) –5, –1, 3, 7…

(iii) \({{1}\over{3}},{{5}\over{3}},{{9}\over{3}},{{13}\over{3}}\)

(iv) 0.6, 1.7, 2.8, 3.9 …

Answer :

(i) 3, 1, –1, –3…

First term = a = 3,

Common difference (d)

= Second term – first term

= Third term – second term

and so on

Therefore, Common difference (d) = 1 – 3 = –2

(ii) –5, –1, 3, 7…

First term = a = –5

Common difference (d)

= Second term – First term

= Third term – Second term

and so on

Therefore, Common difference (d)

= –1 – (–5) = –1 + 5 = 4

(iii)\({{1}\over{3}},{{5}\over{3}},{{9}\over{3}},{{13}\over{3}}\)

First term = a = \({{1}\over{3}}\)

Common difference (d)

= Second term – First term

= Third term – Second term

and so on

Therefore, Common difference (d)

= \({{5}\over{3}} - {{1}\over{3}} = {{4}\over{3}}\)

(iv) 0.6, 1.7, 2.8, 3.9…

First term = a = 0.6

Common difference (d)

= Second term – First term

= Third term – Second term and so on

Therefore, Common difference (d)

= 1.7 - 0.6 = 1.1

- 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 Rs 15 for the first km and Rs 8 for each additional km. (ii) The amount of air present in a cylinder when a vacuum pump removes \(\frac{1}{4}\)th of the air remaining in the cylinder at a time. (iii) The cost of digging a well after every meter of digging, when it costs Rs 150 for the first meter and rises by Rs 50 for each subsequent meter. (iv) The amount of money in the account every year, when Rs 10,000 is deposited at compound Interest at 8% per annum.
- Write first four terms of the AP, when the first term a and 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 = \({{1} \over {2}}\) (v) a = -1.25, d = -0.25
- 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, \({{5}\over{2}}\) , 3, \({{7}\over{2}}\)… (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) \({{-1}\over{2}}, {{-1}\over{2}}, {{-1}\over{2}}, {{-1}\over{2}}\)… (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) \(1^2, 5^2, 7^2, 73\)…

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