Sequences and Series

Sequences and Series

1. Arithmetic Sequence

   • Common Difference (d)
     • Can be found by subtracting two consecutive terms. Ex: U2-U1
   • Un=U1 + (n-1)d
     • U1 can be found when the common difference and any other term of the sequence is given by replacing and rearranging.
     • The common difference (d) can be found when U1 and any other term of the sequence is given by replacing and rearranging.
     • Look for given values in question!
   • Sigma (Σ)
     • Sum of...
     • Sigma Notation
     • Sn=n/2 (2U1 + (n-1)d)
       • Can be used to find d by replacing an rearranging.
       • Look for given values in question!

2. Geometric Sequence

   • Common Ratio (r)
     • Can be found by dividing two consecutive terms. ex: U2/U1
   • Pi (Π)
     • multiplication of...
     • Pi Notation
     • Infinite
       • S∞ = U1/ 1-r
         • IrI < 1
     • Finite
       • Sn= {U1[(r^n) - 1]}/r - 1
         • r≠1
   • Un= U1[r^(n-1)]
     • Look for given values in question! Rearrange to find missing values!

3. Commutative

4. Terms: U1,U2,U3...Un

5. Patterns

6. Sn=sum of n terms

7. State through formulas!

8. By: Laura Garcia Echeverri

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