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NCERT Exemplar · Class 10 Mathematics Arithmetic Progressions

71 questions · 71 still being checked

EXERCISE 5.1 1–10 (part 1 of 8)

  1. Choose the correct answer from the given four options:

    Exercise 1

    In an AP, if d=−4,n=7,an=4\displaystyle d=-4, n=7, a_n=4, then a\displaystyle a is
    (A)
    6\displaystyle 6 (B) 7\displaystyle 7 (C) 20\displaystyle 20
    (D)
    28\displaystyle 28

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    NCERT’s answer
    (D)
    (D) \(\displaystyle 28\)\[a_n = a + (n-1)d \] \[4 = a + (7-1)(-4) \] \[a = 4 + 24 = 28 \]

  2. Exercise 2

    In an AP, if a=3.5,d=0,n=101\displaystyle a=3.5, d=0, n=101, then an\displaystyle a_n will be
    (A)
    0\displaystyle 0 (B) 3.5\displaystyle 3.5
    (C)
    103.5\displaystyle 5
    (D)
    104.5\displaystyle 5

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    NCERT’s answer
    (B)
    (B) \(\displaystyle 3.5\)\[a_n = a + (n-1)d \] \[a_{101} = 3.5 + (101-1)(0) = 3.5 \]

  3. Exercise 3

    The list of numbers -10\displaystyle 10, -6\displaystyle 6, -2\displaystyle 2, 2\displaystyle 2, ... is
    (A)
    an AP with d=−16\displaystyle d=-16
    (B)
    an AP with d=4\displaystyle d=4
    (C)
    an AP with d=−4\displaystyle d=-4
    (D)
    not an AP

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    NCERT’s answer
    (B)
    (B) an AP with \(\displaystyle d=4\)\[-6-(-10) = 4 \] \[-2-(-6) = 4 \] \[2-(-2) = 4 \] Consecutive differences are equal.

  4. Exercise 4

    The 11th \displaystyle 11^{\text {th }} term of the AP: −5,−52,0,52,…\displaystyle -5, \frac{-5}{2}, 0, \frac{5}{2}, \ldots is
    (A)
    -20\displaystyle 20
    (B)
    20\displaystyle 20
    (C)
    -30\displaystyle 30
    (D)
    30\displaystyle 30

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    NCERT’s answer
    (B)
    (B) \(\displaystyle 20\)\[d = \frac{-5}{2}-(-5) = \frac{5}{2} \] \[a_n = a + (n-1)d \] \[a_{11} = -5 + (10)\left(\frac{5}{2}\right) = 20 \]

  5. Exercise 5

    The first four terms of an AP, whose first term is -2\displaystyle 2 and the common difference is -2\displaystyle 2, are
    (A)
    -2\displaystyle 2, 0\displaystyle 0, 2\displaystyle 2, 4\displaystyle 4
    (B)
    -2\displaystyle 2, 4\displaystyle 4, -8\displaystyle 8, 16\displaystyle 16
    (C)
    -2\displaystyle 2, -4\displaystyle 4, -6\displaystyle 6, -8\displaystyle 8
    (D)
    -2\displaystyle 2, -4\displaystyle 4, -8\displaystyle 8, -16\displaystyle 16

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    NCERT’s answer
    (C)
    (C) \(\displaystyle -2, -4, -6, -8\)\[a=-2,\quad d=-2 \] \[a_1=-2,\ a_2=-2+d=-4,\ a_3=-4+d=-6,\ a_4=-6+d=-8 \]

  6. Exercise 6

    The 21st \displaystyle 21^{\text {st }} term of the AP whose first two terms are -3\displaystyle 3 and 4\displaystyle 4 is
    (A)
    17\displaystyle 17
    (B)
    137\displaystyle 137
    (C)
    143\displaystyle 143
    (D)
    -143\displaystyle 143

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    NCERT’s answer
    (B)
    (B) \(\displaystyle 137\)\[d = 4-(-3) = 7 \] \[a_n = a + (n-1)d \] \[a_{21} = -3 + (20)(7) = 137 \]

  7. Exercise 7

    If the 2nd \displaystyle 2^{\text {nd }} term of an AP is 13\displaystyle 13 and the 5th \displaystyle 5^{\text {th }} term is 25\displaystyle 25, what is its 7th \displaystyle 7^{\text {th }} term?
    (A)
    30\displaystyle 30
    (B)
    33\displaystyle 33
    (C)
    37\displaystyle 37
    (D)
    38\displaystyle 38

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    NCERT’s answer
    (B)
    (B) \(\displaystyle 33\)\[a_2 = a + d = 13 \] \[a_5 = a + 4d = 25 \] \[3d = 12 \implies d = 4,\ a = 9 \] \[a_7 = a + 6d = 9 + 24 = 33 \]

  8. Exercise 8

    Which term of the AP: 21\displaystyle 21, 42\displaystyle 42, 63\displaystyle 63, 84\displaystyle 84,... is 210\displaystyle 210?
    (A)
    9th \displaystyle 9^{\text {th }}
    (B)
    10th \displaystyle 10^{\text {th }}
    (C)
    11th \displaystyle 11^{\text {th }}
    (D)
    12th \displaystyle 12^{\text {th }}

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    NCERT’s answer
    (B)
    (B) \(\displaystyle 10^{\text{th}}\)\[a = 21,\quad d = 21 \] \[a_n = a + (n-1)d = 210 \] \[21 + 21(n-1) = 210 \implies n - 1 = 9 \implies n = 10 \]

  9. Exercise 9

    If the common difference of an AP is 5\displaystyle 5, then what is a18−a13\displaystyle a_{18}-a_{13}?
    (A)
    5\displaystyle 5 (B) 20\displaystyle 20
    (C)
    25\displaystyle 25
    (D)
    30\displaystyle 30

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    NCERT’s answer
    (C)
    (C) \(\displaystyle 25\)\[a_{18} - a_{13} = (a+17d) - (a+12d) = 5d \] \[= 5(5) = 25 \]

  10. Exercise 10

    What is the common difference of an AP in which a18−a14=32\displaystyle a_{18}-a_{14}=32?
    (A)
    8\displaystyle 8 (B) -8\displaystyle 8 (C) -4\displaystyle 4 (D) 4\displaystyle 4

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    NCERT’s answer
    (A)
    (A) \(\displaystyle 8\)\[a_{18} - a_{14} = (a+17d)-(a+13d) = 4d = 32 \] \[d = 8 \]