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Answer:
8, 31, 54, 77, 100
Step-by-step explanation:
The arithmetic sequence of 5 terms with first term 8 and last term 100 is 8, 31, 54, 77, 100. An arithmetic sequence is a type of sequence whose difference between its terms is defined by a constant which is commonly represented by d while the terms are represented by a, a+d, a+2d, a+3d and so forth depending on the number of terms of the arithmetic sequence.
Finding the missing terms of an arithmetic sequence:
Given that the arithmetic sequence has 5 terms and the first term is 8 and the last term is 100. Then, 8, ____, _____, ____, 100
Using the first term 8 and the last term 100, find the middle term or the third term using their average such that 8 + 100 ÷ 2 = 108 ÷ 2 = 54. Then, we already have 8, ____, 54, ____, 100.
To get the second term, we may also use the average of the first and third term such that 8 + 54 ÷ 2 = 62 ÷ 2 = 31. Then, we already have 8, 31, 54, ___, 100.
Lastly, find for the fourth term using the average of the third and fifth term such that 54 + 100 ÷ 2 = 154 ÷ 2 = 77.
Completing the arithmetic sequence it will give 8, 31, 54, 77, 100.
To check if the middle terms of this arithmetic sequence is correct, find the difference between the terms and see if they are equal. For instance, 31 - 8 = 23, 54 - 31 = 23, 77 - 54 = 23, and 100 - 77 = 23.
Therefore, the correct arithmetic sequence whose first term is 8 and last term is 100 with 5 terms is 8, 31, 54, 77, 100.