Question

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

Answer 1

Answer :

The required nth term rule of the given linear sequence is (26 - 4n)

Step-by-step explanation :

Given :

Sequence : 22 , 18 , 14 , 10 , 6, ...

To find :

the nth term rule

Solution :

 Let's check if the given sequence is in Arithmetic Progression.

In an A.P., the difference between a term and it's preceding term is constant.

 18 - 22 = -4

 14 - 18 = -4

 10 - 14 = -4

  6 - 10 = -4

The difference is constant. Hence the given sequence is in A.P.

So, in the sequence 22 , 18 , 14 , 10 , 6 ,...

first term, a = 22

common difference, d = -4

nth term of an A.P. is given by,

aₙ = a + (n - 1)d

Now, put the values of a and d,

aₙ = 22 + (n - 1)(-4)

aₙ = 22 - 4n + 4

aₙ = 26 - 4n

Therefore, nth term rule of the given linear sequence is (26 - 4n)

Answer 2

Answer:

Step-by-step explanation:

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given,

the sequence:

22,18,14,10,6

.: by observing we can say that the sequence is in A.P

.: first term (a)= 22

common difference(d)= 18-22= -4

.: nth term of A.P = a+(n-1)d

An = 22+(n-1)-4

= 22-4n+4

= 26-4n

.: nth term = 26-4n