To investigate the pattern in the sequence 5, 20, 80, 320, let's analyze the relationship between the numbers:
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Starting with the first number (5):
- \( 5 \times 4 = 20 \)
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Next step:
- \( 20 \times 4 = 80 \)
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Next step:
- \( 80 \times 4 = 320 \)
From this, we can see that each term in the sequence is multiplied by 4 to yield the next term.
Thus, the rule for this pattern can be expressed as:
\[ \text{next term} = \text{current term} \times 4 \]
In symbolic form, if \( a_n \) represents the nth term in the sequence starting with \( a_1 = 5 \): \[ a_n = 5 \times 4^{(n-1)} \]
So, the next number in the pattern after 320 would be:
\[ 320 \times 4 = 1280 \]
Therefore, the sequence follows the rule of multiplying each term by 4 to find the next term.