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Write first four of the terms of the A.P., when the first term a and the common difference a are given as follows :

(i) a = 10, d = 10

(ii) a = -2, d = 0

(iii) a = 4, d = -3

(iv) a = 12\dfrac{1}{2}, d = 16-\dfrac{1}{6}

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Answer

(i) Here, a1 = a = 10,   a2 = a1 + d = 10 + 10 = 20,

a3 = a2 + d = 20 + 10 = 30,    a4 = a3 + d = 30 + 10 = 40.

Hence, the first four terms of A.P. are 10, 20, 30, 40.

(ii) Here, a1 = a = -2,   a2 = a1 + d = -2 + 0 = -2,

a3 = a2 + d = -2 + 0 = -2,    a4 = a3 + d = -2 + 0 = -2.

Hence, the first four terms of A.P. are -2, -2, -2, -2.

(iii) Here, a1 = a = 4,   a2 = a1 + d = 4 + (-3) = 1,

a3 = a2 + d = 1 + (-3) = -2,    a4 = a3 + d = -2 + (-3) = -5.

Hence, the first four terms of A.P. are 4, 1, -2, -5.

(iv) Here, a1 = a = 12\dfrac{1}{2},   a2 = a1 + d = 12+(16)=26=13\dfrac{1}{2} + \big(-\dfrac{1}{6}\big) = \dfrac{2}{6} = \dfrac{1}{3},

a3 = a2 + d = 26+(16)=16\dfrac{2}{6} + \big(-\dfrac{1}{6}\big) = \dfrac{1}{6},    a4 = a3 + d = 16+(16)\dfrac{1}{6} + \big(-\dfrac{1}{6}\big) = 0.

Hence, the first four terms of A.P. are 12,13,16,0\dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{6}, 0.

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