The exercise below has to do with arithmetic progressions and or arithmetic sequence.
<h3>What is an Arithmetic Progression?</h3>
An arithmetic progression is a sequence of numbers where the difference between each consecutive term remains constant as the sequence progresses.
The next three terms and the rule for finding the <em>nth </em>term in each sequence is given as follows:
A) 1.1,4,9,16,25,36.
The rule for finding the <em>nth </em>term: square each term in the arithmetic series 1², 2², 3², 4², ....nth term = n², etc to get the present term in the sequence.
That is:
1, 4, 9, 16, 25, 36 = 1² 2² 3² 4² 5² 6²
To get the next three terms, we say:
= 7², 8² , 9² = 49, 64, 81
hence, new number sequence 1 , 4, 9, 16, 25, 36, 49, 64, 81.
B) 3, 5, 7, 9,
The rule for finding the nth term here is the Rule for finding the <em>nth </em>term: 2n + 1.
Hence:
3 = 2 (1) + 1 = 3
5 = 2 (2) + 1 = 5
7 = 2 (3) + 1 = 7
9 = 2 (4) + 1 = 9
Therefore the next three terms in the sequence will be arrived at as follows:
2(5) +1 = 10 + 1 = 11
2(6) + 1 = 12 + 1 = 13
2(7) + 1 = 14 + 1 = 15
The updated number sequence is 3, 5, 7, 9, 11, 13, and 15.
C) 20, 16, 12, 8. The next three terms is gotten using the rule (20n-4n). That is:
20 - 4 = 16 = [20 - 4(1) ]
16 - 4 = 12 = [20 - 4(2)]
12 - 4 = 8 = [20 - 4(3)]. Thus the next three terms are:
[20 - 4(4)] = 4
[20 - 4(5)] = 0
[20 - 4(6)] = -4
Hence the updated number sequence is:
20, 16, 12, 8, 4, 0, -4
Learn more about Arithmetic sequences at:
brainly.com/question/1450677
