To find the first five terms in each of the sequences with the given nth terms, you simply need to substitute n with the values 1 through 5. Here are the first five terms for each sequence:
a. 6n - 1
- When n = 1: 6(1) - 1 = 6 - 1 = 5
- When n = 2: 6(2) - 1 = 12 - 1 = 11
- When n = 3: 6(3) - 1 = 18 - 1 = 17
- When n = 4: 6(4) - 1 = 24 - 1 = 23
- When n = 5: 6(5) - 1 = 30 - 1 = 29
So, the first five terms of this sequence are 5, 11, 17, 23, and 29.
b. 3n - 2
- When n = 1: 3(1) - 2 = 3 - 2 = 1
- When n = 2: 3(2) - 2 = 6 - 2 = 4
- When n = 3: 3(3) - 2 = 9 - 2 = 7
- When n = 4: 3(4) - 2 = 12 - 2 = 10
- When n = 5: 3(5) - 2 = 15 - 2 = 13
So, the first five terms of this sequence are 1, 4, 7, 10, and 13.
c. 8n + 1
- When n = 1: 8(1) + 1 = 8 + 1 = 9
- When n = 2: 8(2) + 1 = 16 + 1 = 17
- When n = 3: 8(3) + 1 = 24 + 1 = 25
- When n = 4: 8(4) + 1 = 32 + 1 = 33
- When n = 5: 8(5) + 1 = 40 + 1 = 41
So, the first five terms of this sequence are 9, 17, 25, 33, and 41.
d. 3n² - 1
- When n = 1: 3(1²) - 1 = 3(1) - 1 = 3 - 1 = 2
- When n = 2: 3(2²) - 1 = 3(4) - 1 = 12 - 1 = 11
- When n = 3: 3(3²) - 1 = 3(9) - 1 = 27 - 1 = 26
- When n = 4: 3(4²) - 1 = 3(16) - 1 = 48 - 1 = 47
- When n = 5: 3(5²) - 1 = 3(25) - 1 = 75 - 1 = 74
So, the first five terms of this sequence are 2, 11, 26, 47, and 74.