<s>[INST] I do not understand how to solve this The two sequences of numbers { 1, 4, 16, 64, . . .} and { 3, 12, 48, 192, . . .} are mixed as follows: { 1, 3, 4, 12, 16, 48, 64, 192, . . .}. One of the numbers in the mixed series is 1048576. Then the number immediately preceding it is
 [/INST] The second sequence is just 3 times the previous sequence. Note that no number in the first sequence is divisible by 3 while all numbers in the second are. The mixed sequence is in the form $\{4^0, 3\cdot 4^0, 4^1, 3\cdot 4^1, 4^2, 3 \cdot 4^2, 4^3, 3 \cdot 4^3, \ldots\}$. Seeing that 1048576 is not divisible by 3 it must be from the first sequence. Looking at the mixed set you can see that each $4^k$ is preceded by $3 \cdot 4^{k - 1}$. Since $4^k = 1048576$, $3 \cdot 4^{k - 1} = \frac{3}{4} \cdot 4^k= \frac{3}{4} \cdot 1048576 = 786432$ so the preceding term is 786432 . 
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