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Type the missing number in this sequence:\newline5,  25,  125,  _,  3,125,  15,6255,\; 25,\; 125,\; \_,\; 3,125,\; 15,625

Full solution

Q. Type the missing number in this sequence:\newline5,  25,  125,  _,  3,125,  15,6255,\; 25,\; 125,\; \_,\; 3,125,\; 15,625
  1. Observe pattern in sequence: We observe the pattern in the sequence to determine the rule that generates it. Each number appears to be multiplied by 55 to get the next number.
  2. Check pattern by multiplying: We check the pattern by multiplying the first number by 55: 5×5=255 \times 5 = 25, which matches the second number in the sequence.
  3. Apply rule to find missing number: We continue to check the pattern by multiplying the second number by 55: 25×5=12525 \times 5 = 125, which matches the third number in the sequence.
  4. Calculate missing number: Now, we apply the same rule to find the missing number by multiplying the third number by 55: 125×5125 \times 5.
  5. Verify pattern consistency: We calculate 125×5=625125 \times 5 = 625. This should be the missing number in the sequence.
  6. Confirm pattern correctness: To ensure the pattern is correct, we check the next number by multiplying the missing number we found by 55: 625×5=3,125625 \times 5 = 3,125, which matches the next number in the sequence.
  7. Confirm pattern correctness: To ensure the pattern is correct, we check the next number by multiplying the missing number we found by 55: 625×5=3,125625 \times 5 = 3,125, which matches the next number in the sequence.Finally, we verify the last given number by multiplying 3,1253,125 by 55: 3,125×5=15,6253,125 \times 5 = 15,625, which confirms the pattern is consistent and correct.

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