Arithmetic progressions excercise 5.1

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Question no 2)
Write first four term of the A.P. when the first term of a and the common difference d are given as follows

A) a = 10 d = 10 
Solutions
Let the series of a1, a2,a3, a4,a5.....
a1= a=10 
a2= a1+d
    = 10+10 = 20
a3 = a2+d
     = 20+10 = 30
a4 = a3+d
     = 30+10 = 40 
a5 = a4+d
     = 40+10 = 50
Therefore the series will be 10,20,30,40,50
First four terms of this A.P. will be 10,20,30,40........

B) a= -2 , d= 0
Let the series be a1, a2, a3,a4.......
a1 = a= -2
a2 = a1+d
     = -2+0 =-2
a3 = a2+d
     = -2+0 = -2
a4 = a3+d
     = -2+0 = -2
Therefore the series will be -2,-2,-2,-2
First four terms of the A.P. will be -2,-2,-2,-2......

C) a=4, d= -3
Let the series be a1, a2, a3,a4.......
a1= a = 4
a2= a1+d
    = 4-3  = 1
a3= a2+d 
    = 1-3 = -2
a4 = a3+d
     = -2-3 =-5
First four terms of the A.P. will be 4,1,-2,-5.....

D) a=-1, d=½

Let the series be a1, a2, a3,a4.......
a1= a= -1
a2= a1+d
   = -1+½=-½
a3= a2+d
    =-½+½= 0
a4=a3+d
    =0+½=½
First four terms of the A.P. will be -1,-½,0,½.......

E) a=-1.25, d=-0.25

Let the series be a1, a2, a3,a4.......
a1 = a=-1.25
a2 = a1+d
     = -1.25-.25 = -1.50
a3 = a2+d 
     =-1.50-0.25 = -1.75
a4 = a3+d 
     = -1.75-0.25 = -2.00
First four terms of the A.P. will be -1.25,-1.50,-1.75,-2.00.......

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