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How Do You Find the Next Terms in an Arithmetic Sequence?

Find the next four terms in the sequence '2, 4, 6, 8, ...'

Summary

  1. '2, 4, 6, 8, ....' is the sequence of numbers we start with
  2. The common difference, 'd', for this sequence is '2'
  3. Adding '2' to the '8' will give us the next term in the sequence, 10
  4. We repeat this process to get '12, 14, 16'
  5. So we added the terms '10, 12, 14, 16' to our initial sequence

Notes

    1. '2, 4, 6, 8, ....' is our sequence of numbers
    2. '....' means that our sequence continues after the number '8'
    1. '2, 4, 6, 8, ....' is our sequence of numbers
    2. '....' means that our sequence continues after the number '8'
    1. '2, 4, 6, 8, ....' is our sequence of numbers
    2. '....' means that our sequence continues after the number '8'
    1. '2' and '4' are the first two terms in our sequence, and their difference is '4-2', or '2'
    1. '4' and '6' are the second and third terms in our sequence, and their difference is '6-4', or '2'
    1. '6' and '8' are the third and fourth terms in our sequence, and their difference is '8-6', or '2'
    1. So the common difference between all the terms in the sequence is '2'
    1. Our first four terms are '2, 4, 6, 8'
    2. The common difference between all the terms in the sequence is '2'
    1. Our first four terms are '2, 4, 6, 8'
    2. The common difference between all the terms in the sequence is '2'
    3. So we want to add 'd', or '2', to the '8'
    1. Our first four terms are '2, 4, 6, 8'
    2. The common difference between all the terms in the sequence is '2'
    3. So we want to add 'd', or '2', to the '8'
    4. 8+2=10
    1. So now our sequence looks like this:
    2. '2, 4, 6, 8, 10, ...'
    3. That constant amount of change is our common difference
    1. Up to this point, our sequence looked like this:
    2. '2, 4, 6, 8, 10, ...'
    3. So we want to add 'd', or '2', to the '10'
    4. 10+2=12
    5. So now our sequence looks like this:
    6. '2, 4, 6, 8, 10, 12, ...'
    1. Up to this point, our sequence looked like this:
    2. '2, 4, 6, 8, 10, 12, ...'
    3. 12+2=14
    4. So now our sequence looks like this:
    5. '2, 4, 6, 8, 10, 12, 14, ...'
    1. Up to this point, our sequence looked like this:
    2. '2, 4, 6, 8, 10, 12, 14, ...'
    3. 14+2=16
    4. So now our sequence looks like this:
    5. '2, 4, 6, 8, 10, 12, 14, 16, ...'
    1. Now our sequence looks like this:
    2. '2, 4, 6, 8, 10, 12, 14, 16, ...'
    3. We added the four terms '10, 12, 14, 16' to our existing sequence
    1. Remember that the '....' means that our sequence goes on forever!
    1. Remember that the '....' means that our sequence goes on forever!