Let's find the terms for each sequence step-by-step.
### Sequence a: [tex]\( n^2 + 3 \)[/tex]
#### First 4 Terms
1. For [tex]\( n = 1 \)[/tex]:
[tex]\[
1^2 + 3 = 1 + 3 = 4
\][/tex]
2. For [tex]\( n = 2 \)[/tex]:
[tex]\[
2^2 + 3 = 4 + 3 = 7
\][/tex]
3. For [tex]\( n = 3 \)[/tex]:
[tex]\[
3^2 + 3 = 9 + 3 = 12
\][/tex]
4. For [tex]\( n = 4 \)[/tex]:
[tex]\[
4^2 + 3 = 16 + 3 = 19
\][/tex]
So, the first four terms are: [tex]\( 4, 7, 12, 19 \)[/tex].
#### 10th Term
For [tex]\( n = 10 \)[/tex]:
[tex]\[
10^2 + 3 = 100 + 3 = 103
\][/tex]
The 10th term is [tex]\( 103 \)[/tex].
### Sequence b: [tex]\( 2n^2 \)[/tex]
#### First 4 Terms
1. For [tex]\( n = 1 \)[/tex]:
[tex]\[
2 \times 1^2 = 2 \times 1 = 2
\][/tex]
2. For [tex]\( n = 2 \)[/tex]:
[tex]\[
2 \times 2^2 = 2 \times 4 = 8
\][/tex]
3. For [tex]\( n = 3 \)[/tex]:
[tex]\[
2 \times 3^2 = 2 \times 9 = 18
\][/tex]
4. For [tex]\( n = 4 \)[/tex]:
[tex]\[
2 \times 4^2 = 2 \times 16 = 32
\][/tex]
So, the first four terms are: [tex]\( 2, 8, 18, 32 \)[/tex].
#### 10th Term
For [tex]\( n = 10 \)[/tex]:
[tex]\[
2 \times 10^2 = 2 \times 100 = 200
\][/tex]
The 10th term is [tex]\( 200 \)[/tex].
### Final Results:
For sequence a, [tex]\( n^2 + 3 \)[/tex]
- First 4 terms: [tex]\( 4, 7, 12, 19 \)[/tex]
- 10th term: [tex]\( 103 \)[/tex]
For sequence b, [tex]\( 2n^2 \)[/tex]
- First 4 terms: [tex]\( 2, 8, 18, 32 \)[/tex]
- 10th term: [tex]\( 200 \)[/tex]
