Use differences to find a pattern in the sequence. 4,4,9,20,38,64,99 Assuming that the pattern continues, the eighth term should be?

Use differences to find a pattern in the sequence. 6,9,20,39,66,101,144 Assuming that the pattern continues, the eighth term should be?

cassie19
Sep 6, 2017

#1**+1 **

1) Use differences to find a pattern in the sequence. 4,4,9,20,38,64,99 Assuming that the pattern continues, the eighth term should be?

If you look at the difference between the terms, you get the following:

0, 5, 11, 18, 26, 35......

Now, see the difference between these new terms and you get:

5, 6, 7, 8, 9.......etc. It, therefore, follows that you will add: 10, 11, 12, 13......etc. to the FIRST differences: 35+10 =45, 45+11=56, 56+12=68.........etc. Therefore, your sequence will be:

**4,4,9,20,38,64,99, 144, 200, 268........etc.**

**P.S. You could use this more complicated formula to generate each term:**

**a(n) = 1/6 (n^3 + 9n^2 - 34n + 48).**

2) Use differences to find a pattern in the sequence. 6,9,20,39,66,101,144 Assuming that the pattern continues, the eighth term should be?

Do the same for this one and you will see these differences:

3, 11, 19, 27, 35, 43..............

Now look at the differences between these and you get a CONSTANT of 8. So, you will have:

43+8=51, 51+8=59, 59+8=67.........etc. So your sequence will be:

** 6,9,20,39,66,101,144, 195, 254, 321.........etc. **

**P.S. You could also use this more complicated formula to generate each term:**

**a(n) = 4n^2 - 9n + 11**

Guest Sep 6, 2017

edited by
Guest
Sep 6, 2017

#2**+1 **

**Use differences to find a pattern in the sequence 4,4,9,20,38,64,99, ... Assuming that the pattern? continues, the eighth term should be?**

\(\small{ \begin{array}{lrrrrrrrrrrrrrrrrr} & 4 && 4 && 9 && 20 && 38 && 64 && 99 && {\color{red} 144} && \cdots \\ \text{1. Difference } && 0 && 5 && 11 && 18 && 26 && 35 && {\color{red} 45} && \cdots \\ \text{2. Difference } &&& 5 && 6 && 7 && 8 && 9 && {\color{red} 10} && \cdots \\ \text{3. Difference } &&&& 1 && 1 && 1 && 1 && {\color{red} 1} && \cdots \\ \end{array} } \)

\(\begin{array}{|rcrcr|} \hline 9 &+& {\color{red}1} &=& {\color{red}10} \\ 35&+&{\color{red}10} &=& {\color{red}45} \\ 99&+&{\color{red}45} &=& {\color{red}144} \\ \hline \end{array} \)

The eighth term is **99 + 35 + 9 + 1 = 144**

heureka
Sep 6, 2017