**Find the Arithmetic Sequence When First Term and Common Difference are Given :**

The general form an arithmetic sequence is

a, a + d, a + 2d, a + 3d,...........

a - First term and d - common difference

**Question 1 :**

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

(i) a = 1 0 d = 10

**Solution :**

First term (a₁) = 10

Second term (a₂) = a + d

a₂ = 10 + 10

a₂ = 20

Third term (a₃) = a + 2d

a₃ = 10 + 2(10)

a₃ = 10 + 20

a₃ = 30

Fourth term (a₄) = a + 3d

a₄ = 10 + 3(10)

a₄ = 10 + 30

a₄ = 40

Hence, the first four terms are 10, 20, 30 and 40

(ii) a = -2 d = 0

**Solution :**

First term (a₁) = -2

Second term (a₂) = a + d

a₂ = -2 + 0

a₂ = -2

Third term (a₃) = a + 2d

a_{3} = -2 + 2(0)

a_{3} = -2 + 0

a_{3} = -2

Fourth term (a₄) = a + 3d

a₄ = -2 + 3(0)

a₄ = -2 + 0

a₄ = -2

Hence re the first four terms are -2,-2,-2 and -2

(iii) a = 4 d = -3

**Solution:**

First term (a₁) = 4

Second term (a₂) = a + d

a₂ = 4 + (-3)

a₂ = 1

Third term (a₃) = a + 2d

a_{3} = 4 + 2(-3)

a_{3} = 4 - 6

a_{3} = -2

Fourth term (a₄) = a + 3d

a₄ = 4 + 3(-3)

a₄ = 4 - 9

a₄ = -5

Hence the first four terms are 4, 1, -2 and -5

(iv) a = -1 d = 1/2

**Solution :**

First term (a₁) = -1

Second term (a₂) = a + d

a₂ = -1 + (1/2)

= -1/2

Third term (a₃) = a + 2d

a₃ = -1 + 2(1/2)

a₃ = -1 + 1

a₃ = 0

Fourth term (a₄) = a + 3d

a₄ = -1 + 3(1/2)

a₄ = -1 + (3/2)

a₄ = 1/2

Hence the first four terms are -1, -1/2, 0 and 1/2

(v) a = - 1.25 d = -0.25

**Solution :**

First term (a₁) = -1.25

Second term (a₂) = a + d

= -1.25 + (-0.25)

= -1.25 - 0.25

= -1.50

Third term (a₃) = a + 2d

= -1.25 + 2(-0.25)

= -1.25 - 0.50

= -1.75

Fourth term (a₄) = a + 3d

= -1.25 + 3(-0.25)

= -1.25 - 0.75

= 2

Hence the first four terms are -1.25, -1.50, -1.75 and 2

After having gone through the stuff given above, we hope that the students would have understood, find arithmetic sequence with first term and common difference.

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