Question

Rakesha claims that the equation f(n) =5n-7 is the function notation for the sequence that is represented by the explicit formula a+-2 + 5(n-1) James doesnt understand how this can be the case. Help James by listing the steps to write the explicit formula given sequence in function notation. Provide a rationale for each step.

Answer 1

Step-by-step explanation:

explicit formula for a sequence allows you to find the value of any term in the sequence. ...

A recursive formula for a sequence allows you to find the value of the nth term in the sequence.

if you know the value of the (n-1)th term in the sequence.

A sequence is an ordered list of objects.

.

Answer 2

Question:

Rakesha claims that the equation $f(n) =5n-7$ is the function notation for the sequence that is represented by the explicit formula $a_{n}= -2 + 5(n-1)$ . James doesn't understand how this can be the case. Help James by listing the steps to write the explicit formula given sequence in function notation. Provide a rationale for each step.

Answer:

Arithmetic progression of a sequence $a_{n} =a_{1} +(n-1)d$.

Step-by-step explanation:

Given:

The equation $f(n) =5n-7$ is the function notation for the sequence that is represented by the explicit formula $a_{n}= -2 + 5(n-1)$.

To write the explicit formula given sequence in function notation.

Step 1

According to the question in terms of function,

when $n=1$,

$f(1) = 5*1-7$

$f(1) = -2$

when $n=2$,

$f(2)=5*2-7$

$f(2)=3$

when $n=3$,

$f(3)=5*3-7$

$f(3)=8$

Sequence is $-2, 3, 8, .....$

Step 2

Then the common difference is,

Common difference = second term - first term

⇒  $cd=d_{2} -d_{1}$

∵ $3-(-2)=5$,

$8-3=5$

∴ common difference is 5.

Step 3

$a_{1} =-2$, $d =cd =5$

$a_{n}= -2 + 5(n-1)$

Therefore,

arithmetic progression of a sequence,  

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

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