Question

What is the closed linear form of the sequence 5, 7.5, 10, 12.5, 15,...

A) an = 5 + 2.5n

B) an = 5 - 2.5n

C) an = 2.5 + 2.5n

D) an = 2.5 - 2.5n

Answer 1

C)

`a_n=2.5+2.5n`

EXPLANATION

The given sequence is:

5, 7.5, 10, 12.5, 15,...

where

`a_1=5`

The constant difference is:

`d = 7.5 - 5 = 2.5`

The closed linear form is given by;

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

We substitute the values into the formula to get:

`a_n=5+2.5(n-1)`

Expand to get;

`a_n=5+2.5n - 2.5`

`a_n=2.5+2.5n`

Answer 2

Answer: Option C)

`a_n = 2.5 + 2.5n`

Explanation:

Note that the sequence increases by a factor of 2.5, that is, each term is the sum of the previous term plus 2.5.

`7.5 - 5 = 2.5\\\\10 -7.5 = 2.5\\\\12.5 -10 = 2.5`

therefore this is an arithmetic sequence with an increase factor d = 2.5

The linear formula for the sequence
`a_n` is:

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

Where

`d = 2.5\\\\a_1 = 5`

`a_1` is the first term of the sequence

So

`a_n = 5 + 2.5(n-1)`

`a_n = 2.5 + 2.5n`

The answer is the option C)