Introduction to Sequences

Hello, students! Today we are going to learn about something very fun called sequences. A sequence is a list of numbers that follow a certain order or pattern. For example, if we start with the number 1, the next number could be 2, and then 3, and so on.

What is a Sequence?

A sequence is like a chain of numbers. Each number connects to the next one. Sometimes, we follow a rule to find the next number.

Key Rules for Completing a Sequence

  1. Look at the Pattern: Check how the numbers change. Do they get bigger or smaller?
  2. Count Carefully: Sometimes, we just count up or down.
  3. Use Addition or Subtraction: Many sequences add or take away the same number each time.

Tips and Tricks

  • Count Up: If you see 1, 2, 3, the next number is 4. You are counting up by 1.
  • Count Down: If you see 5, 4, 3, the next number is 2. You are counting down by 1.
  • Skip Counting: Sometimes we skip numbers, like counting by 2s: 2, 4, 6, 8…

Now, let’s practice completing sequences!

Questions

Easy Level Questions

  1. What comes after 1, 2, __?
  2. Fill in the blank: 5, 6, __, 8.
  3. Complete the sequence: 10, 11, __.
  4. What comes next: 3, 4, 5, __?
  5. Fill in the blank: 7, __, 9, 10.
  6. What is next in the sequence: 1, 2, 3, __?
  7. Complete this: 4, __, 6.
  8. What comes after 8, 9, __?
  9. Fill in the blank: 2, __, 4.
  10. Find the next number: 6, 7, 8, __?

Medium Level Questions

  1. Complete the sequence: 12, 14, __, 18.
  2. What comes next: 5, 10, 15, __?
  3. Fill in the blank: 20, 19, __, 17.
  4. Complete this: 3, 6, 9, __.
  5. What comes after: 1, 3, 5, __?
  6. Fill in the blank: 11, __, 13, 14.
  7. Find the next number: 2, 4, 6, __?
  8. Complete the pattern: 9, 8, __, 6.
  9. What comes next: 15, 13, __, 11?
  10. Fill in the blank: 1, 4, 7, __?

Hard Level Questions

  1. Complete the sequence: 2, 4, 8, __, 32.
  2. What comes next: 10, 20, 30, __?
  3. Fill in the blank: 19, 15, __, 11.
  4. Complete this: 5, 10, 15, 20, __.
  5. What comes after: 2, 5, 10, __?
  6. Fill in the blank: 10, 15, __, 25.
  7. Find the next number: 100, 90, 80, __?
  8. Complete the pattern: 1, 2, 4, 8, __?
  9. What comes next: 6, 12, 18, __?
  10. Fill in the blank: 50, 45, __, 35.

Answers and Explanations

Easy Level Answers

  1. Explanation: We count up by 1 from 2.
  2. Explanation: After 6, the next number in counting is 7.
  3. Explanation: 11 comes after 10 when we count up.
  4. Explanation: We continue counting up from 5 to get 6.
  5. Explanation: The number after 7 is 8 in the counting sequence.
  6. Explanation: The next number after 3 is 4 when counting up.
  7. Explanation: We are counting up by 2, so after 4 comes 5.
  8. Explanation: The next number after 9 is 10.
  9. Explanation: The sequence goes up by 2, so the next is 3.
  10. Explanation: Counting up from 8 leads us to 9.

Medium Level Answers

  1. Explanation: The sequence adds 2 each time.
  2. Explanation: We are adding 5 each time.
  3. Explanation: We are counting down by 1 in this sequence.
  4. Explanation: The sequence adds 3 each time.
  5. Explanation: The sequence adds 2 each time.
  6. Explanation: We go up by 2 from 11 to 12.
  7. Explanation: We are adding 2 each time.
  8. Explanation: We are counting down by 1.
  9. Explanation: The sequence goes down by 2 each time.
  10. Explanation: We are counting up by 3 in this sequence.

Hard Level Answers

  1. Explanation: Each number doubles the previous one.
  2. Explanation: We add 10 each time.
  3. Explanation: We are counting down by 4 each time.
  4. Explanation: The sequence goes up by 5 each time.
  5. Explanation: We are doubling the previous number.
  6. Explanation: We add 5 to 15 to get 20.
  7. Explanation: We are counting down by 10 each time.
  8. Explanation: Each number doubles the previous one.
  9. Explanation: We are adding 6 each time.
  10. Explanation: We go down by 5 each time.

I hope you enjoyed learning about sequences! Keep practicing, and you will get better at completing them.