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
a3 = -2 + 2(0)
a3 = -2 + 0
a3 = -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
a3 = 4 + 2(-3)
a3 = 4 - 6
a3 = -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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