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Find the first 5 terms of the sequence given the [tex]\(n\)[/tex]th term.

1. [tex]\(a_n = n + 4\)[/tex]
2. [tex]\(a_n = 2n - 1\)[/tex]
3. [tex]\(a_n = 12 - 3n\)[/tex]
4. [tex]\(a_n = 3^n\)[/tex]
5. [tex]\(a_n = (-2)^n\)[/tex]

Sagot :

GinnyAnsweridn
Sure! Let's find the first 5 terms of each sequence based on the formulas provided.

### Sequence 1: [tex]\( a(n) = n + 4 \)[/tex]
- Term 1: [tex]\( a(1) = 1 + 4 = 5 \)[/tex]
- Term 2: [tex]\( a(2) = 2 + 4 = 6 \)[/tex]
- Term 3: [tex]\( a(3) = 3 + 4 = 7 \)[/tex]
- Term 4: [tex]\( a(4) = 4 + 4 = 8 \)[/tex]
- Term 5: [tex]\( a(5) = 5 + 4 = 9 \)[/tex]

So, the first 5 terms of this sequence are: [5, 6, 7, 8, 9]

### Sequence 2: [tex]\( a(n) = 2n - 1 \)[/tex]
- Term 1: [tex]\( a(1) = 2 \times 1 - 1 = 1 \)[/tex]
- Term 2: [tex]\( a(2) = 2 \times 2 - 1 = 3 \)[/tex]
- Term 3: [tex]\( a(3) = 2 \times 3 - 1 = 5 \)[/tex]
- Term 4: [tex]\( a(4) = 2 \times 4 - 1 = 7 \)[/tex]
- Term 5: [tex]\( a(5) = 2 \times 5 - 1 = 9 \)[/tex]

So, the first 5 terms of this sequence are: [1, 3, 5, 7, 9]

### Sequence 3: [tex]\( a(n) = 12 - 3n \)[/tex]
- Term 1: [tex]\( a(1) = 12 - 3 \times 1 = 9 \)[/tex]
- Term 2: [tex]\( a(2) = 12 - 3 \times 2 = 6 \)[/tex]
- Term 3: [tex]\( a(3) = 12 - 3 \times 3 = 3 \)[/tex]
- Term 4: [tex]\( a(4) = 12 - 3 \times 4 = 0 \)[/tex]
- Term 5: [tex]\( a(5) = 12 - 3 \times 5 = -3 \)[/tex]

So, the first 5 terms of this sequence are: [9, 6, 3, 0, -3]

### Sequence 4: [tex]\( a(n) = 3^n \)[/tex]
- Term 1: [tex]\( a(0) = 3^0 = 1 \)[/tex] (since any number to the power of 0 is 1)
- Term 2: [tex]\( a(1) = 3^1 = 3 \)[/tex]
- Term 3: [tex]\( a(2) = 3^2 = 9 \)[/tex]
- Term 4: [tex]\( a(3) = 3^3 = 27 \)[/tex]
- Term 5: [tex]\( a(4) = 3^4 = 81 \)[/tex]

So, the first 5 terms of this sequence are: [1, 3, 9, 27, 81]

### Sequence 5: [tex]\( a(n) = (-2)^n \)[/tex]
- Term 1: [tex]\( a(0) = (-2)^0 = 1 \)[/tex] (since any number to the power of 0 is 1)
- Term 2: [tex]\( a(1) = (-2)^1 = -2 \)[/tex]
- Term 3: [tex]\( a(2) = (-2)^2 = 4 \)[/tex]
- Term 4: [tex]\( a(3) = (-2)^3 = -8 \)[/tex]
- Term 5: [tex]\( a(4) = (-2)^4 = 16 \)[/tex]

So, the first 5 terms of this sequence are: [1, -2, 4, -8, 16]

### Summary:
- Sequence 1: [5, 6, 7, 8, 9]
- Sequence 2: [1, 3, 5, 7, 9]
- Sequence 3: [9, 6, 3, 0, -3]
- Sequence 4: [1, 3, 9, 27, 81]
- Sequence 5: [1, -2, 4, -8, 16]
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