SolveItClass 10 · NCERT

NCERT Solutions · Class 10 Mathematics Arithmetic Progressions

49 questions · 49 still being checked

EXERCISE 5.2 1–10 (part 2 of 6)

  1. Exercise 1

    Fill in the blanks in the following table, given that a\displaystyle a is the first term, d\displaystyle d the common difference and an\displaystyle a_{n} the n\displaystyle nth term of the AP:
    a\displaystyle ad\displaystyle dn\displaystyle nan\displaystyle a_{n}
    (i)7\displaystyle 73\displaystyle 38\displaystyle 8⋯
    (ii)-18\displaystyle 18⋯10\displaystyle 100\displaystyle 0
    (iii)...-3\displaystyle 318\displaystyle 18-5\displaystyle 5
    (iv)-18.9\displaystyle 18.92.5\displaystyle 2.5⋯3.6\displaystyle 3.6
    (v)3.5\displaystyle 3.50\displaystyle 0105\displaystyle 105⋯
    NCERT’s answer
    (i)
    $\displaystyle a_{n}=28$ (ii) $\displaystyle d=2$ (iii) $\displaystyle a=46$ (iv) $\displaystyle n=10$ (v) $\displaystyle a_{n}=3.5$

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  2. Exercise 2

    Choose the correct choice in the following and justify :
    (i)
    30th term of the AP: 10\displaystyle 10, 7\displaystyle 7, 4\displaystyle 4, . . . , is (A) 97\displaystyle 97 (B) 77\displaystyle 77 (C) -77\displaystyle 77 (D) -87\displaystyle 87
    (ii)
    11\displaystyle 11 th term of the AP:−3,−12,2,…\displaystyle \mathrm{AP}:-3,-\frac{1}{2}, 2, \ldots, is (A) 28\displaystyle 28 (B) 22\displaystyle 22 (C) -38\displaystyle 38 (D) −4812\displaystyle -48 \frac{1}{2}
    NCERT’s answer
    (i)
    C (ii) B

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  3. Exercise 3

    In the following APs, find the missing terms in the boxes :
    (i)
    2\displaystyle 2, □, 26\displaystyle 26
    (ii)
    □, 13\displaystyle 13, □, 3\displaystyle 3
    (iii)
    5\displaystyle 5, □, □, 912\displaystyle 9 \frac{1}{2}
    (iv)
    -4\displaystyle 4, □, □, □, □, 6\displaystyle 6
    (v)
    □, 38\displaystyle 38, □, □, □, -22\displaystyle 22
    NCERT’s answer
    (i)
    $\displaystyle 14$ (ii) $\displaystyle 18$ , $\displaystyle 8$ (iii) $\displaystyle 6 \frac{1}{2}, 8$ (iv) - $\displaystyle 2$ , $\displaystyle 0$ $\displaystyle 2$ , $\displaystyle 4$ (v) $\displaystyle 53,23,8,-7$

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  4. Exercise 4

    Which term of the AP : 3\displaystyle 3, 8\displaystyle 8, 13\displaystyle 13, 18\displaystyle 18, . . , is 78\displaystyle 78?
    NCERT’s answer
    16th term

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  5. Exercise 5

    Find the number of terms in each of the following APs :
    (i)
    7\displaystyle 7, 13\displaystyle 13, 19\displaystyle 19, . . , , 205\displaystyle 205
    (ii)
    18,1512,13,…,−47\displaystyle 18,15 \frac{1}{2}, 13, \ldots,-47
    NCERT’s answer
    (i)
    $\displaystyle 34$ (ii) $\displaystyle 27$

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  6. Exercise 6

    Check whether - 150\displaystyle 150 is a term of the AP : 11\displaystyle 11, 8\displaystyle 8, 5\displaystyle 5, 2\displaystyle 2 …
    NCERT’s answer
    No

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  7. Exercise 7

    Find the 31st term of an AP whose 11th term is 38\displaystyle 38 and the 16th term is 73.
    NCERT’s answer
    $\displaystyle 178$

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  8. Exercise 8

    An AP consists of 50\displaystyle 50 terms of which 3rd term is 12\displaystyle 12 and the last term is 106. Find the 29th term.
    NCERT’s answer
    $\displaystyle 64$

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  9. Exercise 9

    If the 3rd and the 9th terms of an AP are 4\displaystyle 4 and -8\displaystyle 8 respectively, which term of this AP is zero?
    NCERT’s answer
    5th term

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  10. Exercise 10

    The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
    NCERT’s answer
    $\displaystyle 1$

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