What is the value of z in the sequence 1, 2, 4, 8, 10, 20, 22, z, ...?
A. 44
B. 32
C. 24
D. 40
Answer (1)
Let's analyze the sequence given: 1, 2, 4, 8, 10, 20, 22, z, ...
To determine the pattern of the sequence, let's observe the differences and characteristics of the numbers:
The first few numbers (1, 2, 4, 8) seem to double each time. This suggests a pattern of powers of 2. Indeed, these are $2^0 , $2^1 , $2^2 , and $2^3 .
The sequence then jumps to 10 and 20. Observing these numbers, they don't fit the power of 2 pattern, but they have a special relation:
10 is not a power of 2 and neither is 20, but 20 is simply 10 times 2.
Continuing from 20, the number 22 follows. This can be seen as 20 plus 2.
Now, let's conjecture what might come next. Since the transition from 10 to 20 involved doubling and then adding 2 to continue to 22, it seems reasonable to double 22:
22 doubled is 44.
The sequence alternates in patterns, suggesting the value of z is 44.
The answer is option A: 44.
