2. Write the first six terms of the following sequence:

f(n) = (-3)^{n-1}

3. Find the 5th term and the 15th term of the sequence given by:

a_n = 3 - n^2

The first six terms of the sequence defined by f ( n ) = ( − 3 ) n − 1 are 1, -3, 9, -27, 81, and -243. For the sequence a n ​ = 3 − n 2 , the 5th term is -22, and the 15th term is -222.
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Answered by Anonymous | 2025-07-04

To address the question, we need to work through two separate tasks: writing the first six terms of a given sequence and finding specific terms in another sequence.
Task 1: Sequence f ( n ) = ( − 3 ) n − 1
For this sequence, we want to find the first six terms by substituting values of n from 1 to 6.

For n = 1 : f ( 1 ) = ( − 3 ) 1 − 1 = ( − 3 ) 0 = 1

For n = 2 : f ( 2 ) = ( − 3 ) 2 − 1 = ( − 3 ) 1 = − 3

For n = 3 : f ( 3 ) = ( − 3 ) 3 − 1 = ( − 3 ) 2 = 9

For n = 4 : f ( 4 ) = ( − 3 ) 4 − 1 = ( − 3 ) 3 = − 27

For n = 5 : f ( 5 ) = ( − 3 ) 5 − 1 = ( − 3 ) 4 = 81

For n = 6 : f ( 6 ) = ( − 3 ) 6 − 1 = ( − 3 ) 5 = − 243


Thus, the first six terms of the sequence are: 1 , − 3 , 9 , − 27 , 81 , − 243 .
Task 2: Sequence a n ​ = 3 − n 2
To find the 5th and 15th terms, we substitute n = 5 and n = 15 into the formula.

5th Term : a 5 ​ = 3 − ( 5 ) 2 = 3 − 25 = − 22

15th Term : a 15 ​ = 3 − ( 15 ) 2 = 3 − 225 = − 222


Therefore, the 5th term of the sequence is − 22 and the 15th term of the sequence is − 222 .

Answered by LucasMatthewHarris | 2025-07-06