Question

4. 122 is the_th term in the sequence -54, -38, -22, -6, ...

Answer 1

122 is the 12th term in the sequence.

Explanation:

By the looks of it, this is an arithmetic sequence. This is because the difference between each term in the sequence is a constant.

The difference between each term in the sequence is 16 (every term is larger than the one prior to it by 16).

The nth term of an arithmetic sequence can be moduled using the formula:

`a_n = a_1 + (n - 1)d`

In our case, a1 = -54 and d = 16. Therefore:

`a_n = -54 + 16(n - 1)\\\to a_n = -54 + 16n - 16\\\to a_n = -70 + 16n`

To find the index of 122 in the sequence, we'll substitute it as
`a_n` and solve the equation for n.

`122 = -70 + 16n\\192 = 16n\\n = 12`

122 is the 12th term in the sequence.