Answer:
1. Next sequence = 20
2. Tn = 47 - 3n
3. Common number: 32
Explanation:
Given
Sequence 1: 0, 4, 8, 12, 16
Sequence 2: 44, 41, 38, 35, 32
a. Write out the next sequence in (1)
The pattern followed by sequence 1 is that, each successive sequence is and addition of 4 to the previous sequence..
See observation below
4 = 0 + 4
8 = 4 + 4
12 = 8 + 4
16 = 12 + 4
Definitely, the next sequence will be 4 + the previous sequence.
Next sequence = 16 + 4
Next sequence = 20
2. The rule for continuing sequence 2
It'll be observed that sequence 2 follows an arithmetic progression.
To get the rule for continuing the sequence, the following data are needed.
I. The first term of the sequence.
This is often represented by letter a.
a = 44
II. The common difference.
This is the difference between two successive sequence
This is often represented by letter d.
d = 41 - 44 = -3
Or
d = 38 - 44 = -3
Using the arithmetic progression formula
Tn = a + (n - 1)d
By substituting 44 for a and -3 for d.
Tn = 44 + (n - 1)(-3)
Tn = 44 - 3n + 3
Tn = 44 + 3 - 3n
Tn = 47 - 3n
Hence, the rule for continuing the sequence is 47 - 3n where n is the current term of the sequence
III. Work out a number in common in both sequence
It'll be observed that the visible data of sequence 2 are bigger than that of sequence 1.
To get a common number, we have to extend sequence 1 until we arrive at a common number in both sequence
Sequence 1: 0, 4, 8, 12, 16
This becomes
Sequence 1: 0, 4, 8, 12, 16, 20, 24, 28, 32.....
32 is common in sequence (1) and (2).
If the sequence is extended, we'll arrive at another common number. But we have to stop, since we've arrived at a common number.