Question

1) The nth term of a sequence is 25-3n
a) Work out the first three terms.
b) Work out the value of the first negative term.

Answer 1

Answer:

see explanation

Step-by-step explanation:

To find the first 3 terms substitute n = 1, 2, 3 into the formula

(a)

$a_{1}$ = 25 - (3 × 1) = 25 - 3 = 22

$a_{2}$ = 25 - (3 × 2) = 25 - 6 = 19

$a_{3}$ = 25 - (3 × 3) = 25 - 9 = 16

The first three terms are 22, 19, 16

Note the difference between consecutive terms is - 3

19 - 22 = 16 - 19 = - 3

Continuing this pattern

(b)

16 - 3 = 13

13 - 3 = 10

10 - 3 = 7

7 - 3 = 4

4 - 3 = 1

1 - 3 = - 2

The first negative term is - 2

Answer 2

The first three terms and the value of the first negative term of the sequence 25-3n are 22, 19, 16, and -2 respectively.

What are sequences?

Sequences are a group of numbers written in a specific order such that the nth term of the sequence can be determined using some logic or formula.

We can find the first three terms below:

The formula of the sequence is given to be 25-3n.

The first term of the sequence at n = 1 is 25-(3*1) = 22

The second term of the sequence at n = 2 is 25-(3*2) = 19

The third term of the sequence at n = 3 is 25-(3*3) = 16

We can find the first negative term of the sequence below:

For the term to be negative, 3n should be greater than 25.

The multiple of 3 that is greater than 25 is 27. Therefore n = 9.

The 9th term of the sequence is:

25-(3*9) = 25 - 27

= -2

Therefore, we have found the first three terms and the value of the first negative term of the sequence 25-3n are 22, 19, 16, and -2 respectively.

Learn more about sequences here: https://brainly.com/question/7882626

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