How to Find the Nth Term for an Arithmetic Sequence of High Order

Step-by-Step Guide

1. 1

   Step 1: Write down the formula.

   It's an=A+B+C{\displaystyle a_{n}=A+B+C}.
   
   A=first term in the sequence{\displaystyle A={\text{first term in the sequence}}} B=first difference{\displaystyle B={\text{first difference}}} C=second difference{\displaystyle C={\text{second difference}}} n=the n-th term in an arithmetic sequence that you need to find{\displaystyle n={\text{the n-th term in an arithmetic sequence that you need to find}}} You will learn more about A, B, and C in the following steps.
2. 2

   Step 2: Write down the first four terms of the sequence.

     Then, draw a straight line leading toward the first difference or B{\displaystyle B}.
   
   Make sure to leave some space apart each other.
   
   Look at the diagram for help. , Then, write each difference at the end of two lines that lead to the numbers which it came from.  Draw a straight line leading toward the second difference or C{\displaystyle C}. ,  Then, write each difference at the end of two lines that lead to the numbers which it came from. ,{\displaystyle a_{n}=A+B+C.}{\displaystyle } Let us pretend we are searching for the 28th term.
   
   In the diagram, we have a28=5+5+5.{\displaystyle a_{28}=5+5+5.} In the formula, (n−1)C0{\displaystyle {}_{(n-1)}C_{0}} means (n−1)!!∗0!{\displaystyle {\frac {(n-1)!}{!*0!}}} ,  That is your answer! a28=5+5+5{\displaystyle a_{28}=5+5+5} a28=5+5+5.{\displaystyle a_{28}=5+5+5.} a28=5(1)+5(27)+5(351){\displaystyle a_{28}=5(1)+5(27)+5(351)} a28=5+135+1755{\displaystyle a_{28}=5+135+1755} a28=1895{\displaystyle a_{28}=1895}
3. 3

   Step 3: Find the positive difference between each pair of terms.

4. 4

   Step 4: Find the positive difference between the pair of numbers in the second row.

5. 5

   Step 5: Plug in the values in the formula an=A+B+C.

6. 6

   Step 6: Solve the equation.

Detailed Guide

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