Question

Which functions represent the arithmetic sequence 8, 1.5, –5, –11.5 . . . ? Check all that apply.

f(n) = –6.5n + 14.5f(n) = –1.5n + 9.5f(n) = 6.5n + 1.5f(1) = 8, f(n + 1) = f(n) – 6.5f(1) = 8, f(n + 1) = f(n) – 1.5f(1) = 8, f(n + 1) = f(n) + 6.5

Answer 1

Answer:

f(n)= -6.5n +14.5

f(1)= 8, f(n+1) = f(n) - 6.5

Step-by-step explanation:

the arithmetic sequence 8, 1.5, –5, –11.5 . . .

First term is 8

Now we find difference between the terms

1.5 - 8= -6.5

-5-1.5= -6.5

difference is -6.5

The formula is f(n)= a1 + (n-1)d

where a1 is the first term and d is the difference

f(n)= 8 + (n-1)(-6.5)

f(n)= 8 -6.5n+6.5

f(n)= -6.5n +14.5

To get recursive formula we use

f(n+1) = f(n)+ difference

f(1)= 8, f(n+1) = f(n) - 6.5

Answer 2

The functions that represent the arithmetic sequence is given by:

f(n) = –6.5n + 14.5

f(n+1) f(n) – 6.5, f(1) = 8

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In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d, and the nth term is given by:

$f(n) = a_1 + (n-1)d$

• In which $a_1$ is the first term.

The sequence can also be represented by a recursive sequence, given by:

$f(1) = a_1$

$f(n+1) = f(n) - d$

In this sequence:

• The first term is $a_1 = -$
• The common difference is $d = 1.5 - 8 = -6.5$.

Thus, the possible representations are:

$f(n) = a_1 + (n-1)d$

$f(n) = 8 - 6.5(n-1)$

$f(n) = 8 - 6.5n + 6.5$

$f(n) = -6.5n + 14.5$

And

$f(1) = a_1$

$f(n+1) = f(n) - d$

$f(1) = 8$

$f(n+1) = f(n) - 6.5$

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