Question

Enter the first 4 terms of the sequence defined by the given rule. Assume that the domain of each function is the set of whole numbers greater than 0.
f(1) = 9, f(n) = (−3) · f(n − 1) + 15

Answer 1

A function f whose domain is the set of positive integers is called a sequence. The

values

f (1), f (2), f (3),…, ), f (n …

are called the terms of the sequence; f(1) is the first term, f(2) is the second term, f(3)

is the third term, . . . , ) f (n is the nth term, and so on.

Answer 2

The first four terms of the sequence are 9, -12. 51 and -138.

Step-by-step explanation:

Given:

The domain of each function is the set of whole numbers greater than 0.

The sequence defined by the given rule $f(n) = (-3). f( n - 1) + 15.$

The first term $f(1) = 9.$

To Find:

The first four terms of the sequence.

Solution:

As given,the first term $f(1) = 9.$

The first term

$f(1) = 9.$

As given, the sequence defined by the given rule $f(n) = (-3). f( n - 1) + 15.$

The second term;

Putting n=2.

$f(2) = (-3). f( 2 - 1) + 15$

       $= (-3). f( 2 - 1) + 15\\= (-3). f(1) + 15\\=(-3).9+15\\=-27+15\\=-12$

The third term;

Putting n=3.

$f(3) = (-3). f( 3 - 1) + 15$

       $= (-3). f( 3 - 1) + 15\\= (-3). f(2) + 15\\=(-3).(-12)+15\\=36+15\\=51$

The fourth term;

Putting n=4.

$f(4) = (-3). f( 4 - 1) + 15$

       $= (-3). f( 4 - 1) + 15\\= (-3). f(3) + 15\\=(-3).(51)+15\\=-153+15\\=- 138$

Thus,The first four terms of the sequence are 9, -12. 51 and -138.

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