Question

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

Answer 1

Answer: Option C)

$a_n = 2.5 + 2.5n$

Step-by-step 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)

Answer 2

ANSWER

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;

$a_n=5+2.5n - 2.5$

$a_n=2.5+2.5n$