Answer to Question #251674 in Discrete Mathematics for Matheca

Question

(1) Use inductive reasoning to predict the next number in each list.

(a) 1, 4, 9, 16, 25, 36, 49, ?

(b) 2, 7, −3, 2, −8, −3, −13, −8, −18, ?

(c) 1/2, 2/3, 3/4, 4/5, 5/6, 6/7, ?

Answer 1

(1) Let us use inductive reasoning to predict the next number in each list.

(a) It follows that the sequence is defined as $x_n=n^2,$ and hence the next number is $8^2=64.$

(b) It follows that $x_{2n}=5+x_{2n-1}$ and $x_{2n+1}=x_{2n}-10,$ and hence the next number is $-13.$

(c) It follows that the sequence is defined as $x_n=\frac{n}{n+1},$ and hence the next number is $\frac{7}{8}.$