3 years ago
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
admin Staff answered 3 years ago
admin Staff answered 3 years ago
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