Help with this math question, its really bugging me! AHH!?

Question

Describe the pattern in this sequence:

200, 202, 206, 212

Now I know that you add the first number with 2, and then the second with 4 and the third with 6, which is adding them with even numbers but I just can figure out how to describe it!!! Its driving me insane! Please help! Thanks!

Answer 1

Hold on. Don't go insane!!
You described it very well, by showing the reasoning
behind the process (pattern) to get from one to the next.

Here is another approach you could think about.
Start out by putting the numbers you have in a list:
1. 200
2. 202
3. 206
4. 212
5. 220
.......and so on
The number at the left tells where you are in the list.

You could tell how you get from a place in the list
to the next place in the list.
If you use "N" to stand for any particular place, then
"N+1" would be the next place. Try to describe the
pattern for getting to the next place just by talking
about a general position N without actually knowing
what specific number N is.

For example, when N is 3, you add 3 times 2 to get
to the next number in the list. 206 + 2*3 = 212. In
all the numbers you were given, to get to the next
one you add 2 times the place number to get the
next one in the list. You can extend the list by this
pattern. To get from the number in place N you add
2*N to find the next number in the list.

The word often used for "N" is a variable. You can
vary it to whatever you want, but a formula using N
is always true. Here is the formula for this example.

If "whatever" is in position N in the list of numbers,
then "whatever + 2N" is in position N+1 in the list.

Hope this helps you find more ways to talk about
patterns in number sequences.

Answer 2

you know, i would describe it as the pattern continues as the multiples of 2s became higher

2 x 1 = 200 --> 202
2 x 2 = 202 --> 206
2 x 3 = 206 --> 212

so if my pattern is right, the next number should be 2 x 4 = 8 so 212 + 8 = 220

:)

Answer 3

Write down the following sentence:- "The difference between terms is '2n', where 'n' is the term number."

For example term 1 is 200 so difference is 2 x1 = 2
Second example term 3 is 206 so difference is 2 x 3 = 6 &c.,

Answer 4

Since you already know how the pattern works, here is the formula:
x(n+1) = x(n) + 2(n + 1), where x(0) = 200