Make a conclusion by induction for the following number sequences.

a) -4, -1, 4, 11,...

-4=1^2-5

-1=2^2-5

4=3^2-5

11=4^2-5

b) 4, 5, 7, 11,...

4=2^0+3

5=2^1+3

7=2^2+3

11=2^3+3

c) 5, 12, 21, 32,...

5=4(1)+1

12=4(2)+4

21=4(3)+9

32=4(4)+16

d) 3, 8, 17, 30,...

3=3(1)+2(0)^2

8=3(2)+2(1)^2

17=3(3)+2(2)^2

30=3(4)+2(3)^2

1 Answers

Best Answer

Step 1

a) Given sequency -4, -1, 4, 11,...

first term t_1=-4=1^2-5

second term t_2=-1=2^2-5

third term t_3=4=3^2-5

fourth term t_4=11=4^2-5

n^(th) term t_n=n^2-5

b) Given Sequaence 4, 5, 7, 11,...

first term t_1=4=2^0+3

second term t_2=5=2^1+3

third term t_3=7=2^2+3

fourth term t_4=11=2^3+3

n^(th) term t_n=2^n-1+3