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How Do You Find the Nth Term in an Arithmetic Sequence?

Find the twentieth term in the sequence 2, 4, 6, 8, ...

Summary

  1. Our sequence is 2, 4, 6, 8
  2. So 'd' is the common difference, which is 2
  3. So this formula will give us the nth term in an arithmetic sequence without having to manually add up to the the nth term!
  4. In this case, 'n' is 20, since we're looking for the 20th term
  5. We see that our 20th term equals 40

Notes

    1. No need to rewrite the sequence!
    1. Our sequence is 2, 4, 6, 8
    1. Our sequence is 2, 4, 6, 8
    1. Our sequence is 2, 4, 6, 8
    2. There's a difference of 2 between 2 and 4
    1. Our sequence is 2, 4, 6, 8
    2. There's a difference of 2 between 2 and 4, as well as between 4 and 6
    1. Our sequence is 2, 4, 6, 8
    2. There's a common difference of 2 between 2 and 4, 4 and 6, and 6 and 8
    1. Our sequence is 2, 4, 6, 8
    2. There's a common difference of 2 between 2 and 4, 4 and 6, and 6 and 8
    1. Our sequence is 2, 4, 6, 8
    2. There's a common difference of 2 between 2 and 4, 4 and 6, and 6 and 8
    3. We'll call the common difference 'd'
    1. Our sequence is 2, 4, 6, 8
    2. There's a common difference of 2 between 2 and 4, 4 and 6, and 6 and 8
    3. We'll call the common difference 'd'
    4. We just need to keep adding 2 until we hit the 20th term!
    1. There must be a way we can determine the 20th term without having to continuously add 2 to each term until we reach the 20th
    1. There is a formula we can use to determine the 20th term without having to continuously add 2 to each term until we reach the 20th!
    1. There is a formula we can use to determine the 20th term without having to continuously add 2 to each term until we reach the 20th!
    1. There is a formula we can use to determine the 20th term without having to continuously add 2 to each term until we reach the 20th!
    2. Here, 'd' is the common difference, 2, and 'n' is the 20 since we're looking for the 20th term
    3. 'a1' is the first term, and 'an' should be 'a20' , which is the 20th term
    1. Our formula is: an = a1 + (n-1)d
    2. Here, 'd' is the common difference, 2, and 'n' is the 20 since we're looking for the 20th term
    3. 'a1' is the first term, and 'an' should be 'a20' , which is the 20th term
    1. Our sequence is 2, 4, 6, 8
    2. Our formula is: an = a1 + (n-1)d
    3. 'a1' is the first term, which is 2
    1. Our sequence is 2, 4, 6, 8
    2. Our formula is: an = a1 + (n-1)d
    3. 'a1' is the first term, which is 2
    4. 'a2' is the second term, which is 4
    1. Our sequence is 2, 4, 6, 8
    2. Our formula is: an = a1 + (n-1)d
    3. 'a1' is the first term, which is 2
    4. 'a2' is the second term, which is 4
    5. 'a3' is the first term, which is 6
    6. 'a4' is the first term, which is 8
    1. Our sequence is 2, 4, 6, 8
    2. Our formula is: an = a1 + (n-1)d
    3. 'a1' is the first term, which is 2
    4. 'a2' is the second term, which is 4
    5. 'a3' is the first term, which is 6
    6. 'a4' is the first term, which is 8
    7. 'an' should be 'a20' , which is the 20th term
    1. Our sequence is 2, 4, 6, 8
    2. Our formula is: an = a1 + (n-1)d
    3. 'a1' is the first term, which is 2
    4. 'an' should be 'a20' , which is the 20th term
    1. Our sequence is 2, 4, 6, 8
    2. Our formula is: an = a1 + (n-1)d
    3. 'a1' is the first term, which is 2
    4. 'an' should be 'a20' , which is the 20th term
    1. Our sequence is 2, 4, 6, 8
    2. Our formula is: an = a1 + (n-1)d
    3. 'a1' is the first term, which is 2
    4. 'an' should be 'a20' , which is the 20th term
    1. Our sequence is 2, 4, 6, 8
    2. Our formula is: an = a1 + (n-1)d
    3. 'a1' is the first term, which is 2
    4. 'an' should be 'a20' , which is the 20th term
    5. (n-1)d = (20-1)d
    6. Remember, 'd' is the common difference, 2
    1. Remember, 'd' is the common difference, 2
    2. (n-1)d = (20-1)2 = (19)2 = 38
    1. Remember, 'd' is the common difference, 2
    2. Our formula is: an = a1 + (n-1)d
    3. 'a1' is the first term, which is 2
    4. (n-1)d = (20-1)2 = (19)2 = 38
    1. This could take a while!
    2. Our sequence is 2, 4, 6, 8
    3. Remember, 'd' is the common difference, 2
    1. This means that our easy formula gave us the same answer without having to add all of the terms up manually!
    2. Our formula is: an = a1 + (n-1)d
    1. This means that our easy formula gave us the same answer without having to add all of the terms up manually!
    2. Our formula is: an = a1 + (n-1)d