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Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the A.P. Q.1

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How i solve the question of arithmetic progressions of ncert of class 10th How i solve the class 10th question of exercise 5.2 Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the A.P.

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  1. (i) Given,

    First term, a = 7

    Common difference, d = 3

    Number of terms, n = 8,

    We have to find the nth term, an = ?

    As we know, for an A.P.,

    an = a+(n−1)d

    Putting the values,

    => 7+(8 −1) 3

    => 7+(7) 3

    => 7+21 = 28

    Hence, an = 28

    (ii) Given,

    First term, a = -18

    Common difference, d = ?

    Number of terms, n = 10

    Nth term, an = 0

    As we know, for an A.P.,

    an = a+(n−1)d

    Putting the values,

    0 = − 18 +(10−1)d

    18 = 9d

    d = 18/9 = 2

    Hence, common difference, = 2

    (iii) Given,

    First term, a = ?

    Common difference, d = -3

    Number of terms, n = 18

    Nth term, an = -5

    As we know, for an A.P.,

    an = a+(n−1)d

    Putting the values,

    −5 = a+(18−1) (−3)

    −5 = a+(17) (−3)

    −5 = a−51

    a = 51−5 = 46

    Hence, a = 46

    (iv) Given,

    First term, a = -18.9

    Common difference, d = 2.5

    Number of terms, n = ?

    Nth term, an = 3.6

    As we know, for an A.P.,

    an = a +(n −1)d

    Putting the values,

    3.6 = − 18.9+(n −1)2.5

    3.6 + 18.9 = (n−1)2.5

    22.5 = (n−1)2.5

    (n – 1) = 22.5/2.5

    n – 1 = 9

    n = 10

    Hence, n = 10

    (v) Given,

    First term, a = 3.5

    Common difference, d = 0

    Number of terms, n = 105

    Nth term, an = ?

    As we know, for an A.P.,

    an = a+(n −1)d

    Putting the values,

    an = 3.5+(105−1) 0

    an = 3.5+104×0

    an = 3.5

    Hence, an = 3.5

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