What is the nth term rule of the linear sequence below? 27 , 25 , 23 , 21 , 19 , . .

-2n + 29

Step-by-step explanation:

27,25,23,21,19

-2difference

-2n + 29

-2 x (1 ) + 29 =27

-2 x (3) +29 =23

 The required n-th term is 25+2n.

Step-by-step explanation:  We are given to find the n-th term of the following linear sequence :

27,   25,   23,   21,   19,   .   .    .

We note from the given sequence that

So, the given sequence is an arithmetic sequence with first term 27 and common difference, 2.

We know that the n-th term of an arithmetic sequence with first term a and common difference d is given by

For the given sequence, we have

a = 27  and  d = 2.

Therefore, the n-th term of the given sequence is

Thus, the required n-th term is 25+2n.

19-6n

Step-by-step explanation:

a is 13 that is,first term

Common difference is 2nd term -1st term which is -6

Formula is a+(n-1)d

13+(n-1)-6

For simplification open the bracket

13-6n+6

19-6n

23

Step-by-step explanation:

-9, -5, -1, 3, 7, 11, 15, 19, 23

3n-8

Step-by-step explanation:

general term=3n - 8

7n-1

Step-by-step explanation:

Nth term=6+7(n-1)

Nth=6-7+7n

Nth term=-1+7n

Nth term=7n-1

8n+7

Step-by-step explanation:

= 6n - 5

Step-by-step explanation:

There is a common difference d between the consecutive terms, that is

d =7 - 1 =  13 - 7 = 19 - 13 = 25 - 19 = 6

This indicates the sequence is arithmetic with n th term

= a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 1 and d = 6, thus

= 1 + 6(n - 1) = 1 + 6n - 6 = 6n - 5

Step-by-step explanation:

Since this sequence starts with -5 and decreases by 2 with each term, its rule would be:

Hope this helps!