Ive been working through a book and got most questions until i got to these, and i am just in a rut do not have the skills to get out of it, please help guys. Thanks

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- Jan 17th 2011, 03:43 PM #1

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## Help Please, in a rut.

Ive been working through a book and got most questions until i got to these, and i am just in a rut do not have the skills to get out of it, please help guys. Thanks

- Jan 17th 2011, 04:24 PM #2

- Jan 17th 2011, 04:32 PM #3

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- Jan 17th 2011, 04:35 PM #4

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- Jan 17th 2011, 04:40 PM #5
This might help

Read #8, #11

http://www.mathhelpforum.com/math-he...hp?do=vsarules

- Jan 17th 2011, 05:35 PM #6

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Hello, Mathswoman!

I'll get you started . . .

#12 is a matter of Observation . . . look and see the pattern.

12. Write down the difference between consecutive pairs of term in the sequence

and describe the new sequence that has been found.

(a) Square numbers.

$\displaystyle \begin{array}{ccccccccccccc} \hline

\text{Squares:} & 1 && 4 && 9 && 16 && 25 && 36 \\ \hline

\text{Differences:} && 3 && 5 && 7 && 9 && 11 \\ \hline \end{array}$

The differences are consecutive odd numbers.

. . The $\displaystyle \,n^{th}$ difference is: .$\displaystyle 2n+1$

(b) Triangular Numbers

$\displaystyle \begin{array}{ccccccccccccccc} \hline

\text{Triangulars:} & 1 && 3 && 6 && 10 && 15 && 21 && 28 \\ \hline

\text{Differences:} && 2 && 3 && 4 && 5 && 6 && 7 \\ \hline\end{array}$

The differences are consecutive integers.

. . The $\displaystyle \,n^{th}$ difference is: .$\displaystyle n+1$

(c) Powers of two

$\displaystyle \begin{array}{ccccccccccccccc} \hline

\text{Powers of 2:} & 2 && 4 && 8 && 16 && 32 && 64 && 128 \\ \hline

\text{Differences:} && 2 && 4 && 8 && 16 && 32 && 64 \\ \hline\end{array}$

The differences are consecutive powers of 2.

. . The $\displaystyle \,n^{th}$ difference is: .$\displaystyle 2^n$

(d) Powers of three

$\displaystyle \begin{array}{ccccccccccccccc} \hline

\text{Powers of 3:} & 3 && 9 && 27 && 81 && 243 && 729 \\ \hline

\text{Differences:} && 6 && 18 && 54 && 192 && 496 \\

&& 2\cdot3 && 2\cdot3^2 && 2\cdot3^3 && 2\cdot3^4 && 2\cdot 3^5 \\ \hline\hline\end{array}$

The differences are twice a power of 3..

. . The $\displaystyle \,n^{th}$ difference is: .$\displaystyle 2\cdot 3^n$

(e) Fibonacci numbers

$\displaystyle \begin{array}{ccccccccccccccccc} \hline

\text{Fibonacci:} & 1 && 1 && 2 && 3 && 5 && 8 && 13 && 21\\ \hline

\text{Differences:} && 0 && 1 && 1 && 2 && 3 && 5 && 8 \\ \hline\end{array}$

The differences are consecutive Fibonacci numbers.

. . The $\displaystyle \,n^{th}$ difference is: .$\displaystyle F_{n-1$