Answer with Step-by-step explanation:
[tex]a) {n}^{2} + 3 \\ \\ n = 1 \\ {1}^{2} + 3 \\ 1 + 3 \\ = 4 \\ \\ n = 2 \\ {2}^{2} + 3 \\ 4 + 3 \\ = 7 \\ \\ n = 3 \\ {3}^{2} + 3 \\ 9 + 3 \\ = 12 \\ \\ n = 4 \\ {4}^{2} + 3 \\ 16 + 3 \\ = 19 \\ \\ n = 10 \\ {10}^{2} + 3 \\ 100 + 3 \\ = 103[/tex]
In this sequence,
1st term = 4
2nd term = 7
3rd term = 12
4th term = 19
10th term = 103
[tex]b)2 {n}^{2} \\ \\ n = 1 \\ 2 \times {1}^{2} \\ 2 \times 1 \\ = 2 \\ \\ n = 2 \\ 2 \times {2}^{2} \\ 2 \times 4 \\ = 8 \\ \\ n = 3 \\ 2 \times {3}^{2} \\ 2 \times 9 \\ = 18 \\ \\ n = 4 \\ 2 \times {4}^{2} \\ 2 \times 16 \\ = 32 \\ \\ n = 10 \\ 2 \times {10}^{2} \\ 2 \times 100 \\ = 200[/tex]
in this sequence,
1st term = 2
2nd term =8
3rd term = 18
4th term =32
10th term = 200
