Question

Use inductive reasoning to determine the next two terms in each sequence: a) 1, 3, 7, 15, 31 ....

Answer 1

Answer: 63, 127

Step-by-step explanation: 1+2=3; 3+4=7; 7+8=15; 15+16=31; 31+32=63; 63+64=127

Or, if we call the first value a1 , the sequence is given by an=2n−1

The first approach to analyzing almost any sequence is to look at the differences of successive elements. In this sequence, that’s 2, 4, 8, 16, 32. That makes the answers above pretty easy.

Answer 2

63,127

Explanation:

the interval between each number is multiplied by 2

such as between 1 and 3 we have 2 so 2×2=4

the 4+3=7 and so on