Question

In a sequence, each number after the first number is obtained by adding 4 to the previous number. If the first number in the sequence is 7, which of the following expressions represents the nth number in the sequence?

Answer 1

`T_n = 3+ 4n`

Explanation:

From the question, we understand that:

`T_1 = 7` ---- First Term

`d = 4` ---- Common difference

Required

Determine the nth term

nth term of a sequence is calculated using:

`T_n = T_1 + (n - 1)d`

Substitute values for
`T_1` and
`d`

`T_n = 7 + (n - 1) * 4`

Open bracket

`T_n = 7 + 4n - 4`

Collect Like Terms:

`T_n = 7 - 4+ 4n`

`T_n = 3+ 4n`

Hence, the nth term of the sequence is:

`T_n = 3+ 4n`