Final answer:
To find the first five terms of the sequences with given nth terms, values 1 through 5 are substituted into each expression, resulting in the first five terms for each sequence. The constant sequence c yields the same term for its first five values.
Step-by-step explanation:
The student has asked to find the first five terms in sequences given their respective nth terms.
- a. 2n² + 6: By substituting n = 1, 2, 3, 4, 5 we get the terms 8, 20, 38, 62, 92.
- b. 4n + 1: By substituting n = 1, 2, 3, 4, 5 we get the terms 5, 9, 13, 17, 21.
- c. 10¹ - 3: This sequence is constant because there is no n term involved, so the first five terms are all 999,999,997.
- d. 3n - 1: By substituting n = 1, 2, 3, 4, 5 we get the terms 2, 5, 8, 11, 14.
This exercise helps the student understand how to calculate terms of a sequence by substituting values of n into the given nth term.