advance funtions and models Sequence and series

If it's an arithmetic sequence, then all terms differ by the same value.
So, what value do you discover by subtracting A[sub:kv9z9w6o]3[/sub:kv9z9w6o] from A[sub:kv9z9w6o]4[/sub:kv9z9w6o] ?

Once discovered, how many of that value is the difference between A[sub:kv9z9w6o]12[/sub:kv9z9w6o] and A[sub:kv9z9w6o]4[/sub:kv9z9w6o]
or A[sub:kv9z9w6o]12[/sub:kv9z9w6o] and A[sub:kv9z9w6o]3[/sub:kv9z9w6o] ?

You will not know the value exactly until you know "m" and "n", but you can write the answers in terms of "m" and "n".
 
th difference is m +2n bt is there not a formula so i mont have to multipl it 12 times what happends when the #'s get bigger lik 50....
 
the difference is all you need from the information you are working with.
A[sub:3bia5oop]3[/sub:3bia5oop] + 9(m+2n) or A[sub:3bia5oop]4[/sub:3bia5oop] + 8(m+2n) is A[sub:3bia5oop]12[/sub:3bia5oop].

You can also get a general formula for any term, say the 50th one.
You have to know the equation for A[sub:3bia5oop]k[/sub:3bia5oop] for that,
or alternatively A[sub:3bia5oop]k[/sub:3bia5oop]=A[sub:3bia5oop]3[/sub:3bia5oop]+(m+2n)(k-3).

The first term is A[sub:3bia5oop]1[/sub:3bia5oop] which is A[sub:3bia5oop]3[/sub:3bia5oop]-2(m+2n).
A[sub:3bia5oop]k[/sub:3bia5oop] is A[sub:3bia5oop]1[/sub:3bia5oop] + (k-1)(m+2n).

If you understand this pattern, you'll find it straightforward.

It isn't a case of "multiplying lots of times", the multiplication is only done once.
A[sub:3bia5oop]3[/sub:3bia5oop]+9(m+2n)=A[sub:3bia5oop]12[/sub:3bia5oop].
You just add 2n to m, multiply that by 9 in this case and add the answer to A[sub:3bia5oop]3[/sub:3bia5oop] to find A[sub:3bia5oop]12[/sub:3bia5oop].

You only need find "multiples of the difference".

2, 5, 8, 11......
To find any term, add on the appropriate multiple of 3 to the first term.
 
so if the problem doesnt have and equation with variables bt i get how you subtracted what you needed to multiply EX. in an arithmetic progression the first term is -45 and the common difference is 15. what is the 45th term and the nth term?
 
If you do it without the formula, you can say

T[sub:247wnpsa]2[/sub:247wnpsa]=-45+15
T[sub:247wnpsa]3[/sub:247wnpsa]=-45+15+15=-45+2(15)
T[sub:247wnpsa]4[/sub:247wnpsa]=-45+15+15+15=-45+3(15).

At that point, you may be noticing a PATTERN.

The formula is an expression for that pattern that you only need to place "k" the term number into.
Or you can say... for the first term, I don't add 15,
for the second one I add 15, for the third I add twice 15, for the 4th I add 3 times 15 and so on.

The number of 15's you add is always 1 less than k, which is k-1.

So the formula for the term of an arithmetic sequence is

T[sub:247wnpsa]k[/sub:247wnpsa]=T[sub:247wnpsa]1[/sub:247wnpsa]+(k-1)(difference between terms).

Then in your example, T[sub:247wnpsa]45[/sub:247wnpsa]=-45+44(15)
The nth term is T[sub:247wnpsa]n[/sub:247wnpsa]=T[sub:247wnpsa]1[/sub:247wnpsa]+(n-1)(difference)
 
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