The exercise below has to do with arithmetic progressions and or arithmetic sequence.
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 nth term in each sequence is given as follows:
A) 1.1,4,9,16,25,36.
The rule for finding the nth 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 nth 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:
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