SolveItClass 10 · NCERT

NCERT Solutions · Class 10 Mathematics Arithmetic Progressions

49 questions · 49 still being checked

EXERCISE 5.1 1–4 (part 1 of 6)

  1. Exercise 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 ₹ 15\displaystyle 15 for the first km and ₹ 8\displaystyle 8 for each additional km.
    (ii)
    The amount of air present in a cylinder when a vacuum pump removes 14\displaystyle \frac{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\displaystyle 150 for the first metre and rises by ₹ 50\displaystyle 50 for each subsequent metre.
    (iv)
    The amount of money in the account every year, when ₹ 10000\displaystyle 10000 is deposited at compound interest at 8\displaystyle 8 % per annum.
    NCERT’s answer
    (i)
    Yes. $\displaystyle 15$, $\displaystyle 23$, $\displaystyle 31$, ... forms an AP as each succeeding term is obtained by adding $\displaystyle 8$ in its preceding term. (ii) No. Volumes are $\displaystyle \mathrm{V}, \frac{3 \mathrm{~V}}{4},\left(\frac{3}{4}\right)^{2} \mathrm{~V}, \ldots$ (iii) Yes. $\displaystyle 150$, $\displaystyle 200$, $\displaystyle 250$, ... form an AP. (iv) No. Amounts are $\displaystyle 10000\left(1+\frac{8}{100}\right), 10000\left(1+\frac{8}{100}\right)^{2}, 10000\left(1+\frac{8}{100}\right)^{3}, \ldots$

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  2. Exercise 2

    Write first four terms of the AP, when the first term a\displaystyle a and the common difference d\displaystyle d are given as follows:
    (i)
    a=10,d=10\displaystyle a=10, \quad d=10
    (ii)
    a=−2,d=0\displaystyle a=-2, \quad d=0
    (iii)
    a=4,d=−3\displaystyle a=4, \quad d=-3
    (iv)
    a=−1,d=12\displaystyle a=-1, d=\frac{1}{2}
    (v)
    a=−1.25,d=−0.25\displaystyle a=-1.25, d=-0.25
    NCERT’s answer
    (i)
    $\displaystyle 10$, $\displaystyle 20$, $\displaystyle 30$, $\displaystyle 40$ (ii) -$\displaystyle 2$,-$\displaystyle 2$,-$\displaystyle 2$,-$\displaystyle 2$ (iii) $\displaystyle 4$, $\displaystyle 1$, -$\displaystyle 2$, -$\displaystyle 5$ (iv) $\displaystyle -1,-\frac{1}{2}, 0, \frac{1}{2}$ (v) -$\displaystyle 1.25$, -$\displaystyle 1.50$, -$\displaystyle 1.75$, -$\displaystyle 2.0$

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  3. Exercise 3

    For the following APs, write the first term and the common difference:
    (i)
    3,1,−1,−3,…\displaystyle 3,1,-1,-3, \ldots
    (ii)
    −5,−1,3,7,…\displaystyle -5,-1,3,7, \ldots
    (iii)
    13,53,93,133,…\displaystyle \frac{1}{3}, \frac{5}{3}, \frac{9}{3}, \frac{13}{3}, \ldots
    (iv)
    0.6\displaystyle 6, 1.7\displaystyle 1.7, 2.8\displaystyle 2.8, 3.9\displaystyle 3.9, . . .
    NCERT’s answer
    (i)
    $\displaystyle a=3, d=-2$ (ii) $\displaystyle a=-5, d=4$ (iii) $\displaystyle a=\frac{1}{3}, d=\frac{4}{3}$ (iv) $\displaystyle a=0.6, d=1.1$

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  4. Exercise 4

    Which of the following are APs ? If they form an AP, find the common difference d\displaystyle d and write three more terms.
    (i)
    2,4,8,16,…\displaystyle 2,4,8,16, \ldots
    (ii)
    2,52,3,72,…\displaystyle 2, \frac{5}{2}, 3, \frac{7}{2}, \ldots
    (iii)
    -1.2\displaystyle 1.2,-3.2\displaystyle 3.2,-5.2\displaystyle 5.2,-7.2\displaystyle 7.2,...
    (iv)
    -10\displaystyle 10,-6\displaystyle 6,-2,2\displaystyle 2,2,...
    (v)
    3,3+2,3+22,3+32,…\displaystyle 3,3+\sqrt{2}, 3+2 \sqrt{2}, 3+3 \sqrt{2}, \ldots
    (vi)
    0.2,0.22,0.222,0.2222,…\displaystyle 0.2,0.22,0.222,0.2222, \ldots
    (vii)
    0,−4,−8,−12,…\displaystyle 0,-4,-8,-12, \ldots
    (viii)
    −12,−12,−12,−12,…\displaystyle -\frac{1}{2},-\frac{1}{2},-\frac{1}{2},-\frac{1}{2}, \ldots
    (ix)
    1,3,9,27,…\displaystyle 1,3,9,27, \ldots
    (x)
    a,2a,3a,4a,…\displaystyle a, 2 a, 3 a, 4 a, \ldots
    (xi)
    a,a2,a3,a4,…\displaystyle a, a^{2}, a^{3}, a^{4}, \ldots
    (xii)
    2,8,18,32,⋯\displaystyle \sqrt{2}, \sqrt{8}, \sqrt{18}, \sqrt{32}, \cdots
    (xiii) 3,6,9,12,…\displaystyle \sqrt{3}, \sqrt{6}, \sqrt{9}, \sqrt{12}, \ldots
    (xiv) 12,32,52,72,…\displaystyle 1^{2}, 3^{2}, 5^{2}, 7^{2}, \ldots
    (xv) 12,52,72,73,…\displaystyle 1^{2}, 5^{2}, 7^{2}, 73, \ldots
    NCERT’s answer
    (i)
    No (ii) Yes. $\displaystyle d=\frac{1}{2} ; 4, \frac{9}{2}, 5$ (iii) Yes. $\displaystyle d=-2 ;-9.2,-11.2,-13.2$ (iv) Yes. $\displaystyle d=4 ; 6,10,14$ (v) Yes. $\displaystyle d=\sqrt{2} ; 3+4 \sqrt{2}, 3+5 \sqrt{2}, 3+6 \sqrt{2}$ (vi) No (vii) Yes. $\displaystyle d=-4$; -$\displaystyle 16$, -$\displaystyle 20$, -$\displaystyle 24$ (viii) Yes. $\displaystyle d=0 ;-\frac{1}{2},-\frac{1}{2},-\frac{1}{2}$ (ix) No (x) Yes. $\displaystyle d=a ; 5 a, 6 a, 7 a$ (xi) No (xii) Yes. $\displaystyle d=\sqrt{2} ; \sqrt{50}, \sqrt{72}, \sqrt{98}$ (xiii) No (xiv) No (xv) Yes. $\displaystyle d=24 ; 97,121,145$

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