Question

What is the closed linear form for this sequence given a1 = 0.3 and an + 1 = an + 0.75?

Answer 1

Answer:

The closed linear form of the given sequence is $a_{n}=0.75n-0.45$

Step-by-step explanation:

Given that the first term $a_{1}=0.3$ and $a_{n+1}=a_{n}+0.75$

To find the closed linear form for the given sequence

The formula for arithmetic sequence is

$a_{n}=a_{1}+(n - 1)d$  (where d is the common difference)

The above equation is of the given form  $a_{n+1}=a_{n}+0.75$

Comparing this we get d=0.75

With $a_{1}=0.3$ and d=0.75

We can substitute these values in $a_{n}=a_{1}+(n - 1)d$

$a_{n}=a_{1}+(n - 1)d$

$=0.3+(n-1)(0.75)$

$=0.3+0.75n-0.75$

$=-0.45+0.75n$

Rewritting as below

$=0.75n-0.45$

Therefore $a_{n}=0.75n-0.45$

Therefore the closed linear form of the given sequence is $a_{n}=0.75n-0.45$