Question

Write the n,th term of an Arithmetic sequence is 8n-4.write the sequence

Answer 1

Answer:

4 , 12 , 20 , 28 ...

Step-by-step explanation:

Given,

nth term of an Arithmetic sequence = 8n - 4

To Find :-

The sequence

How To Do :-

We need to equate the '8n - 4' to the general form of a term in an A.P after equating we can observe that the equation satisfies for any value of 'n'. So we need to put the value of 'n' as '1' because then 'd' will become zero , So we can easily find the value of 'a'. After getting the value of 'a' we need to put the value of 'n' as 2 and we need to substitute the values of both 'n' and 'a'. After obtaining the value of 'd' we need to find the sequence of an A.P

Formula Required :-

nth term of an A.P :-

a_n = a + (n - 1)d

The sequence of the A.P is :-

a , a + d , a + 2d + a + 3d ...

Solution :-

a + (n - 1)d = 8n - 4

[ ∴ a_n = a + (n - 1)d]

We can say that , the equation satisfies for any value of 'n' :-

Substituting the  value of 'n' = 1 :-

a + (1 - 1)d = 8(1) - 4

a + (0)d = 8 - 4

a + 0 = 4

a = 4

∴ First term = a = 4

Substituting the value of 'n' = 2 :-

a + (2 - 1)d = 8(2) - 4

4 + (1)d = 16 - 4

[ ∴ a = 4 ]

4 + d = 12

d = 12 - 4

d = 8

∴ Common difference = d = 8.

The sequence of the A.P is :-

a , a + d , a + 2d + a + 3d ...

a = 4

a + d = 4 + 8

= 12

a + 2d = 4 + 2(8)

= 4 + 16

= 20

a + 3d = 4 + 3(8)

= 4 + 24

= 28

∴ The sequence of the A.P is :-

4 , 12 , 20 , 28 ...