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High School Mathematics - 2
3.2 Arithmetic Sequence

Arithmetic Sequence
  • Is a sequence such as 3,7,11,15,.....99 or 5,10,15,20,25.....2000 which has a constant difference between terms.
  • The first term is written as a1,
  • The 5th term is written as a5,
  • The 10th terms is written as a10 and
  • The difference is written as d.
Term Number 1 2 3 4 ..... n
Term of Arithmetic Series a1 a2 a3 a4 ..... an
Term of Arithmetic Series a1 a1 + d a1 + 2d a1 + 3d ..... an + (n-1)d
Example 2 6 10 14 ..... 2 + (n-1)4

a1
a2 = a1 + d
a3 = a2 + d = (a1 + d) + d = a1 + 2d
a4 = a3 + d = (a2 + d) + d = a1 + 3d
a5 = a1 + 4d
a6 = a1 + 5d
a7 = a1 + 6d
........
an = a1 + (n-1)d

The formula to find the nth term in Arithmetic series is
a + (n-1)d

Example: 2, 6, 10, 14 ..........
Here
d = a2 - a1 = 4
a1 =2
a2 = 6
a3 = 10
a4 = 14
a5 = 18
a10 = 38
a101 = a + (n-1)d = 2 + (101-1)4 = 2 + 100 x 4 =2 + 400 = 402

Directions: Find d, a1, a5 or a101 for the following arithmetic sequence. Also write at least 5 examples of your own.
Q 1: Find d, a1, a5 for the following arithmetic sequence:
5, 8, 11, 14, 17...............3n+2
d=3,a1=5, a5= 20
d=5,a1=2, a5= 20
d=4,a1=5, a5= 18

Q 2: Find d, a1, a5 for the following arithmetic sequence:
5.3, 5.7, 6.1, 6.5.............
d=0.2,a1=5.3, a5= 6.8
d=0.4,a1=5.3, a5= 6.9
d=4,a1=5.3, a5= 10.5

Q 3: Find d, a1, a5 for the following arithmetic sequence:
a, a+2, a+4, a+6..............2n+a-2
d=a,a1=a, a5= n+8
d=n,a1=a, a5= n+8
d=2,a1=a, a5= a+8

Q 4: Find d, a1, a5, a101 for the following arithmetic sequence:
1,4,7,10,13,16,..............
d = 5, a1=1, a5= 15, a10=28,a101=301
d = 3, a1=1, a5= 13, a10=28,a101=301
d = 3, a1=1, a5= 23, a10=38,a101=201

Q 5: Find d, a1, a5 for the following arithmetic sequence:
7,11,15,19,...............4n+3
d=4, a1=7, a5= 23
d=3, a1=7, a5= 22
d=5, a1=7, a5= 24

Q 6: Find d, a1, a5 for the following arithmetic sequence:
1,5/4,3/2,7/4,...............(n+3)/4
d=1/4,a1=1, a5= 2
d=1/4,a1=1, a5= 8/5
d=1/3,a1=1, a5= 2/3

Q 7: Find d, a1, a5, a101 for the following arithmetic sequence:
-1,10,21,32,43,54,.................
d = 10, a1=-2, a5= 44, a10=88,a101=999
d = 11, a1=-1, a5= 43, a10=98,a101=1099
d = 9, a1=-1, a5= 45, a10=99,a101=1199

Q 8: Find d, a1, a5 for the following arithmetic sequence:
2,-3,-8,-13,...............7-5n
d=-5, a1=2, a5= -18
d=-4, a1=7, a5= -23
d=5, a1=7, a5= 13

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