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5 votes
(04.06 LC)

The first four terms of a sequence are shown below:
8, 5, 2, -1
Which of the following functions best defines this sequence? (5 points)
f(n) = - 3(n-1) +8; for n 2 1
O f(n) = 3(n-1) +8; for n 2 1
O f(n) = - 5(n-1) +8; for n 2 1
f(n) = 5(n-1) +8; for n 2 1

User Lindon Fox
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1 Answer

5 votes

Given:

The first four terms of a sequence are:

8, 5, 2, -1

To find:

The function that defines the given sequence.

Solution:

We have,

8, 5, 2, -1

The differences between two consecutive terms are:


5-8=-3


2-5=-3


-1-2=-3

The given sequence has a common difference -3. It means the given sequence is an arithmetic sequence with first term 8 and common difference -3.

The nth terms of an arithmetic sequence is:


f(n)=a+(n-1)d, for
n\geq 1

Where, a is the first term and d is the common difference.

Putting
a=8,d=-3, we get


f(n)=8+(n-1)(-3)


f(n)=8-3(n-1)


f(n)=-3(n-1)+8, for
n\geq 1

Therefore, the correct option is A.

User The Hog
by
7.4k points

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