FIND THE ARITHMETIC SEQUENCE WHEN FIRST TERM AND COMMON DIFFERENCE ARE GVIEN

The general form an arithmetic sequence is 

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

a - First term and d - common difference

Question :

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

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