Question

PLEASE HELP, I HAVE TO PASS!!!!!!

Position Value of Term
1 7
2 10
3 13
4 16
5 19
6 22

Which expression gives the number in the nth position in the sequence?
A) 2n - 2
B) 3n + 4
C) 4n - 1
D) 5n

Answer 1

3n+4
3(3)+4
9+4
13
is the B).

Answer 2

Option B is correct

3n+4[/tex]

Explanation:

The nth term for the arithmetic sequence is given by:

`a_n = a_1 +(n-1)d` ....[1]

where,

`a_n` is the nth position

n is the number of term

`a_1` is the first term and

d is the common difference.

Given the table:

Position(n) Value of Term(
`a_n`)

1 7

2 10

3 13

4 16

5 19

6 22

from the given table:

At n = 1 ,

`a_1 = 7`

At n = 2

`a_2 = 10`

at n = 3

`a_3 = 13` and so on

Common difference(d) for the sequence is 3

Since,

`d = a_2-a_1=a_3-a_2.....`

⇒
`d = 10-7=13-10......... = 3`

Substitute d = 3 and
`a_1 = 7` in [1] we have;

`a_n = 7+(n-1)(3)`

⇒
`a_n = 7+3n-3`

⇒
`a_n =3n+4`

Therefore, the expression gives the number in the nth position in the sequence is,
`3n+4`