Cyclic Patterns Part 2 Quiz

Cyclic Patterns Part 2 Quiz explores the fascinating idea that numbers often repeat themselves in predictable ways. A fun bit of trivia: in old mechanical clocks, gears were designed using cyclic sequences to ensure accurate timekeeping. This clever use of pattern repetition meant that each rotation or “cycle” brought the system back to its starting point, perfectly synchronized. The same principle appears in math cyclic pattern problems, where repetition leads to beautiful predictability. You will experience how logic meets rhythm in mathematics, where each cycle follows its own musical beat. If the pattern repeats every 9 terms, which term will be same as 100th term captures the essence of such cyclic reasoning explored here.

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Launch Cyclic Patterns Part 2 Quiz

Cyclic Patterns Part 2

If the pattern repeats every 9 terms, which term will be same as 100th term?

What is the units digit of 8⁵³?

What is the units digit of 6⁵⁶?

If the days of a 10-day week are A, B, C, D, E, F, G, H, I, J, what will be the day 437 days after C?

In the sequece below what is the 1000th term:
1 → A, 2 → B, … 26 → Z, 27 → A, and so on.

In the sequence of unit digits of 7¹, 7², 7³ ..., what is the unit digit of 7²⁰²⁵?

The remainders when powers of 3 are divided by 7 form a repeating sequence. What is the remainder when 3¹⁰⁰ is divided by 7?

A clock shows 6:00 pm now. What will the time be after 2000 hours?

The unit digits of 13ⁿ repeat in a cycle. What is the last digit of 13¹⁴⁵?

In the repeating pattern of the digits of π (3.1415926...), the 100th digit after the decimal is 9. What would be the 200th digit if the same 100-digit pattern repeats indefinitely?

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Sample Questions from This Quiz

  1. If the pattern repeats every 9 terms, which term will be same as 100th term?
  2. What is the units digit of 8⁵³?
  3. What is the units digit of 6⁵⁶?
  4. If the days of a 10-day week are A, B, C, D, E, F, G, H, I, J, what will be the day 437 days after C?
  5. In the sequece below what is the 1000th term:
    1 → A, 2 → B, … 26 → Z, 27 → A, and so on.

Try the full quiz and see how many of these you can answer!

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