Question

.What is the nth term rule of the linear sequence below? 22 , 18 , 14 , 10 , 6 , . . .

Answer 1

The nth term rule of the given linear sequence, 22, 18, 14, 10, 6, is nth term = 22 - 4(n-1).

Step-by-step explanation:

The linear sequence given is 22, 18, 14, 10, 6. To find the nth term rule, we can observe that each term is decreasing by 4. Therefore, the nth term rule is:

nth term = 22 - 4(n-1)

For example, to find the 8th term, we substitute n=8 into the nth term rule:

8th term = 22 - 4(8-1) = 22 - 4(7) = 22 - 28 = -6

Answer 2

`a_n=26-4n`

Step-by-step explanation:

The nth term of an AP is

`a_n=a+(n-1)d`

where, a is the first term of the sequence and d is common difference.

The given linear sequence is

22 , 18 , 14 , 10 , 6 , . . .

Here, first term is 22 and common difference is

`d=a_2-a_1=18-22=-4`

The common difference of the sequence is -4. So, the nth term of given sequence is

`a_n=22+(n-1)(-4)`

`a_n=22-4n+4`

`a_n=26-4n`

Therefore, the nth term of the sequence is
`a_n=26-4n`.