1. ## 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

2. Have you tried these?

Post your workings, I'm interested on what you have done.

3. 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.

4. Ive tryed, i justt have no clue what to do because it's all abstract math if you know what i mean

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