what is the next number in the sequence 2,3,7,16,32,______ .
To find the next number in the sequence 2, 3, 7, 16, 32, ______, we need to look for a pattern or relationship between the numbers.
Looking at the sequence, we can observe that each number is obtained by multiplying the previous number by a specific factor and then adding a constant value. Let's break down the pattern step by step:
1. The first term is 2.
2. To find the second term, we multiply the first term (2) by 1 and add 1: (2 x 1) + 1 = 3.
3. To find the third term, we multiply the second term (3) by 2 and add 1: (3 x 2) + 1 = 7.
4. To find the fourth term, we multiply the third term (7) by 2 and add 2: (7 x 2) + 2 = 16.
5. To find the fifth term, we multiply the fourth term (16) by 2 and add 2: (16 x 2) + 2 = 32.
From this pattern, we can see that each term is obtained by multiplying the previous term by 2 and then adding 1 or 2. Therefore, to find the next term, we will multiply the fifth term (32) by 2 and then add 2:
(32 x 2) + 2 = 64 + 2 = 66.
Therefore, the missing number in the sequence is 66.