Question

If first term a and common difference d of an AP in given as follows, then find next four terms of that series.

(i) a = -1, d = 1/2

(ii) a = 1/3 , d = 4/3

(iii) a = 0.6 , d = 1.1

(iv) a = 4, d = -3

(v) a = 11, d = -4

(vi) a = – 1.25, d = -0.25

(vii) a = 20, d = -3/4

Answer 1

(i) Given a = -1, d = 1/2

First term (a) = -1

Second term (a + d) =-1 + 1/2 = -(-1/2)

Third term (a + 2d) = -1 + 2 × 1/2 = 0

Fourth term (a + 3d) = -1 + 3 × 1/2

= -1 + 3/2

= (-2 + 3)/2 = 1/2

Thus, First four terms of A.P. are – 1, – 1/2, 0 and 1/2.

(ii) Given a = 1/3, d = 4/3

First term (a) = 1/3

(iii) Given a = 0.6, d = 1.1

First term (a) = 0.6

Second  term (a + d) = 0.6 + 1.1 = 1.7

Third terms (a + 2d) = 0.6 + 2 × 1.1 = 2.8

Fourth term (a + 3d) = 0.6 + 3 × 1.1 = 3.9

Hence, four terms of A.P are 0.6, 1.7, 2.8 and 3.9.

(iv) Given a = 4, d = -3

First term (a) = 4

Second term (a + d) = 4 + (-3) = 1

Third term (a + 2d) = 4 + 2 (-3) = 4 – 6 = -2

Fourth term (a + 3d) = 4 + 3(-3) = 4 – 9 = -5

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

(v) Given a = 11, d = -4

First term (a) = 11

Second term (a + d) = 11 + (-4) = 11 – 4 = 7

Third terms (a + 2d) = 11 + 2 (-4) = 11 – 8 = 3

Fourth terms (a + 3d) = 11 + 3 (-4) = 11 – 12 = -1

Hence, first four terms of A.P. are 11, 7, 3 and -1

(vi) Given a = -1.25, d = -0.25

First term (a) = -1.25

Second (a + d) = -1.25 + (-0.25)

= -1.25 – 0.25 = -1.50

Third term (a + 2d)

= -1.25 + 2 (-0.25)

= -1.25 – 0.50 = – 1.75

Fourth term (a + 3d) = -1.25 + 3(-0.25)

= -1.25 – 0.75 = – 2.00

Hence first four terms of A.P. are -1.25, -1.50, -1.75 and -2.00.

(vii) Given a = 20, d = -3/2

First Term (a) = 20