# Thread: Confusing number pattern table

1. ## Confusing number pattern table

This is my test paper question:

Row 1 1(squared) = (0 x 2)

Row 2 2(squared) = (1 x 3)

Row 3 3(squared) = (2 x 4)

Row 4 4(squared) = (3 x 5)

Row n ...............................................

(a) In the table, write down an expression, in terms of n, for Row n. (1)

(b) Simplify fully your expression for Row n. You must show all your working.

........................ (2)

2. What does the expression "2(squared)" mean?
$2^2=4$ so it cannot be that.

3. Well, let's take a closer look at these rows:

Row 1 is:

$1^2 = (0 * 2)$

What's something that we can get from this? How about we try to see how these numbers relate to the initial number being squared?

$0 = 1 - 1$

$2 = 1 + 1$

Row 2 is:

$2^2 = (1 * 3)$

$1 = 2 - 1$

$3 = 2 + 1$

Seeing the pattern? It seems that the parentheses hold the number before the initial number times the number right after it. Now, we can take a look at how they actually compare to the real squares of the number:

Row 1: $0 * 2 = 0$

$1^2 = 1$

Row 2: $1 * 3 = 3$

$2^2 = 4$

Here's another pattern, it seems to yield one minus the actual square of the number. So, let's use what we know to configure the nth row:

Row n:

a) $n^2 = [(n - 1) * (n + 1)]$

b) $(n-1)(n+1)$

Use any method to multiply it out and you get:

$n^2 - n + n - 1$

$n^2 - 1$

It seems that the pattern generalizations were correct.

There you go.

[Though this isn't true I do suspect that this is merely to find the pattern and nothing more.]

4. Thanks alot! That really helped!!

5. ## Different question

Also, this compound interest topic seems to confuse me alot!

7. On July 1st 2004, Jack invested £2000 at 5% per annum compound interest.

Work out the value of Jack's investment on July 1st 2006.

£..................

Well I can't find the compound interest formula, and even if I did I would have no idea how to use it! I used to know this topic off by heart but now it just confuses me.

6. The formula for compound interest in this aspect is:

$A = P(1 + r)^t$

$A = \text{Amount after time t}$

$P = \text{Principal amount, or starting amount}$

$r = \text{Annual interest rate (as a decimal)}$

$t = \text{Time in years}$

So, we find out what we know:

$A = ?$

$P = 2000$

$r = .05$

$t = 2$

Ok, we plug in what we know:

$A = 2000(1.05)^2$

$A = 2205$

And there you go.

7. ## Thanks!

Thanks a lot, but how did you get 2 for the year part? Is that because it is 2 years between 2004 and 2006?

Thanks for the help! This much for now.

Vardan

8. That would be correct.

The Interest formula only cares about how many years passed, not what the years actually were. This formula was meant for time in years.