Question

see the pattern given below
1×5=3inta mukalil 2-4

2×6=4inta mukalil 2-4
3×7=5nta mukalil 2-4
a) write the next two lines following this pattern.
b) write the above relation with the help of algebra.
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Answer 1

Answer:

Number Pattern Explorations

Age 7 to 14

You've probably come across number patterns before; ones like :-

2 4 6 8 10 12 . . .

512 256 128 64 32 . . .

220 210 200 190 180 170 . . .

11 14 17 20 23 26 . . .

Work out the rules that produced each of the patterns.

What could be the reason for the series of dots appearing after each one?

Well, let's form some patterns of our own. But this time we will use two maths operations [for the maths person 'operations' mean adding, multiplying, dividing, subtracting etc.] to produce each new number in the pattern. You can probably multiply, add, subtract and divide. Because dividing sometimes can leave bits left over, let's ignore that one for the time being.

Adding put together with subtracting results in something that we could have got just by adding or subtracting. Let me show you:-

Suppose you decided that you would add 5 and subtract 2 each time . . . . then you might as well just be adding 3 each time.

OR suppose you decided to add 6 and subtract 11 each time . . . . then you might as well just be taking away 5 each time.

I therefore suggest that we make a rule about the two operations that we will use for this exploration.

RULE 1 You will use multiplication with either adding or subtraction. BUT you can have the multiplication last if you like.

So let's get started, you will need to do 5 things for this work:

a) You need to choose a STARTING NUMBER (In my example suppose it's 7)

b) You need to decide which OPERATION to do first [addition, subtraction or multiplication] (In my example suppose it's multiplication )

c) You need to decide what NUMBER to use with the operation you chose in b (In my example suppose it's 3 )

d) You need to decide on your next OPERATION (I chose to use multiplication before so it's got to be addition or subtraction, suppose it's subtraction)

e) You need to decide what NUMBER to use with the operation you chose in d. (In my example suppose it's 3)

Let's run through this a bit.

Starting number 7 [ x 3 - 3 ] gives 18

Now we use 18..... [ x 3 - 3 ] gives 51

Now we use 51..... [ x 3 - 3 ] gives 150

I think it would be better to write it down without the brackets bit, although we do have to do both operations before we write the result down and it would be helpful to write it all out in columns going down:-