Question

Write first four terms of the A.P. when the first term a and the common difference d are given as follows
(1) a = 10, d = 10
(2) a = − 2, d = 0
(3) a = 4, d = − 3
(4) a = − 1 d =\(\frac{1}{2}\)
(5) a = − 1.25, d = − 0.25

Answer 1

(i) Given: First term \(a = 10\), common difference \(d = 10\). The series is represented as \(a_1 , a_2 , a_3 , a_4 , a_5\) … The first term, \(a_1 = a = 10\). The second term, \(a_2 = a_1 + d = 10 + 10 = 20\). The third term, \(a_3 = a_2 + d = 20 + 10 = 30\). The fourth term, \(a_4 = a_3 + d = 30 + 10 = 40\). The fifth term, \(a_5 = a_4 + d = 40 + 10 = 50\). Therefore, the series is 10, 20, 30, 40, 50 … The first four terms of this arithmetic progression (A.P.) are 10, 20, 30, and 40.

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(ii) Given: First term \(a = -2\), common difference \(d = 0\). The series is represented as \(a_1 , a_2 , a_3 , a_4\) … The first term, \(a_1 = a = -2\). The second term, \(a_2 = a_1 + d = -2 + 0 = -2\). The third term, \(a_3 = a_2 + d = -2 + 0 = -2\). The fourth term, \(a_4 = a_3 + d = -2 + 0 = -2\). Therefore, the series is -2, -2, -2, -2 … The first four terms of this A.P. are -2, -2, -2, and -2.

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(iii) Given: First term \(a = 4\), common difference \(d = -3\). The series is represented as \(a_1 , a_2 , a_3 , a_4\) … The first term, \(a_1 = a = 4\). The second term, \(a_2 = a_1 + d = 4 - 3 = 1\). The third term, \(a_3 = a_2 + d = 1 - 3 = -2\). The fourth term, \(a_4 = a_3 + d = -2 - 3 = -5\). Therefore, the series is 4, 1, -2, -5 … The first four terms of this A.P. are 4, 1, -2, and -5.

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(iv) Given: First term \(a = -1\), common difference \(d = \frac{1}{2}\). The series is represented as \(a_1 , a_2 , a_3 , a_4\) … The first term, \(a_1 = a = -1\). The second term, \(a_2 = a_1 + d = -1 + \frac{1}{2} = \frac{-1}{2}\). The third term, \(a_3 = a_2 + d = \frac{-1}{2} + \frac{1}{2} = 0\). The fourth term, \(a_4 = a_3 + d = 0 + \frac{1}{2} = \frac{1}{2}\). The series is \(-1 , \frac{-1}{2}, 0, \text{ and } \frac {1}{2}\). The first four terms of this A.P. are \(-1 , \frac{-1}{2}, 0, \text{ and } \frac {1}{2}\).

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(v) Given: First term \(a = -1.25\), common difference \(d = -0.25\). The series is represented as \(a_1, a_2, a_3, a_4\)… The first term, \(a_1 = a = -1.25\). The second term, \(a_2 = a_1 + d = -1.25 - 0.25 = -1.50\). The third term, \(a_3 = a_2 + d = -1.50 - 0.25 = -1.75\). The fourth term, \(a_4 = a_3 + d = -1.75 - 0.25 = -2.00\). The series is -1.25, -1.50, -1.75, -2.00 … The first four terms of this A.P. are -1.25, -1.50, -1.75, and -2.00.