To find the corresponding term in pattern G when the number in pattern H is 48, we need to first understand the relationship between the two patterns.
Pattern H is 4, 8, 12, 16, ..., which is an arithmetic sequence where each term increases by 4.
We can denote the nth term of pattern H as: \[ H_n = 4n \]
To find out which term corresponds to 48, we set: \[ H_n = 48 \] \[ 4n = 48 \] \[ n = 12 \]
Now that we know the term in pattern H that corresponds to 48 is the 12th term, we need to find the 12th term in pattern G.
Pattern G is 2, 4, 6, 8, ..., which is also an arithmetic sequence where each term increases by 2.
The nth term of pattern G can be expressed as: \[ G_n = 2n \]
So, for the 12th term of pattern G: \[ G_{12} = 2 \times 12 = 24 \]
Therefore, when the number in pattern H is 48, the corresponding term in pattern G is 24.
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