# Help Please, in a rut.

• Jan 17th 2011, 02:43 PM
Mathswoman
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, 03:24 PM
pickslides
Have you tried these?

Post your workings, I'm interested on what you have done.
• Jan 17th 2011, 03:32 PM
Mathswoman
I just cant do it i dont understand how to make this into maths that i can work out, ive did the others and these i cant get i dont know i just cant think of it in my head.
• Jan 17th 2011, 03:35 PM
Mathswoman
Ive tryed, i justt have no clue what to do because it's all abstract math if you know what i mean
• Jan 17th 2011, 03:40 PM
pickslides
• Jan 17th 2011, 04:35 PM
Soroban
Hello, Mathswoman!

I'll get you started . . .

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

Quote:

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: .$\displaystyle 2n+1$

Quote:

(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: .$\displaystyle n+1$

Quote:

(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: .$\displaystyle 2^n$

Quote:

(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: .$\displaystyle 2\cdot 3^n$

Quote:

(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: .$\displaystyle F_{n-1$