# What is the next five terms of each arithmetic sequence?

a(1)=6, d=-2
a(1)=2/3, d=-1/3
a(1)=5/7, d=3/7

1) In arithmetic sequence nth  term = a + (n - 1)d.

Where a is first term and d is common difference.

First term = 6 and common difference = 2

a = 6, d = 2

Second term = a + d

= 6 + 2

2nd term = 8

Third term = a + 2d

= 6 + 2(2)

= 6 + 4

3rd term = 10

Fourth term = a + 3d

= 6 + 3(2)

= 6 + 6

4th term = 12

Fifth term = a + 4d

= 6 + 4(2)

= 6 + 8

5th term = 14

The sequence is 6, 8, 10, 12, 14....

2) In arithmetic sequence nth  term = a + (n - 1)d.

Where a is first term and d is common difference.

First term = 2/3 and common difference = - 1/3

a = 2/3, d = - 1/3

Second term = a + d

= (2/3) + (- 1/3)

= (2 - 1)/3

2nd term = 1/3

Third term = (2/3) + 2(- 1/3)

= (2/3) + (- 2/3)

3rd term= 0

Fourth term = a + 3d

= (2/3) + 3(- 1/3)

= (2/3) - 1

= ( 2 - 3)/3

4th term = - 1/3

Fifth term = a + 4d

= (2/3) + 4(- 1/3)

= (2/3) - (4/3)

5th term = - 2/3

The sequence is 2/3, 1/3, 0, -1/3, -2/3....

3) In arithmetic sequence nth  term = a + (n - 1)d.

Where a is first term and d is common difference.

First term = 5/7 and common difference = 3/7

a = 5/7, d = 3/7

Second term = a + d

= (5/7) + (3/7)

2nd term = 8/7

Third term = (5/7) + 2(3/7)

= (5/7) + (6/7)

3rd term= 11/7

Fourth term = a + 3d

= (5/7) + 3(3/7)

= (5/7) + (9/7)

4th term = 14/7

Fifth term = a + 4d

= (5/7) + 4(3/7)

= (5/7) + (12/7)

5th term =  17/7

The sequence is 5/7, 8/7, 11/7, 14/7, 17/7....