Step 1: Understanding Number Sequences
A number sequence is an ordered list of numbers following a particular pattern or rule. The goal is to find the next term based on the pattern.
Step 2: Analyze the given sequence
Sequence: \[ 5, \quad 10, \quad 40, \quad 320, \quad ... \] Find the pattern by checking the ratios between terms: \[ \frac{10}{5} = 2, \quad \frac{40}{10} = 4, \quad \frac{320}{40} = 8. \] The multipliers are doubling each time: 2, 4, 8.
Step 3: Predict the next multiplier
Following the pattern, the next multiplier should be: \[ 8 \times 2 = 16. \]
Step 4: Calculate the next term
Multiply the last term by 16: \[ 320 \times 16 = 5120. \]
Step 5: Conclusion
The next number in the sequence is 5120.