Math: I am trying to figure out nth term. I have answer but do not know what nth term is.?

Question

The sequences:
a) 7,49,343,2401,16807,117649,823543
Is the nth term the ninth term?
What would be the nth term for this sequence?
b) 4,12,20,28
c)2,6,12,20

Answer 1

They are just looking for a formula that lets you calculate the 1st, 2nd, ....nth term in the sequence; if you plug in any integer for n, you should get a value for the term in the n'th position

a) 1st number is 7^1
2nd number is 7^2
...
n'th number is 7^n

b) 1st number is 4*1
2nd number is 4*3 or (4)(2*2 -1)
3rd number is 4*5 or (4)(2*3 - 1)
...
n'th number is 4*(2*n - 1)

Answer 2

Think of the nth term as follows.
You can see that you have a sequence of numbers. You can actually state a specific term from the sequence. Like
2,4,6,8

What is the second term in this sequence
That would be 4

Now imagine I had the ability to pinpoint from the sequence anywhere, the second term all the way to the one hundred and state the value. It would take too much time for me to list all of the values in the sequence. Instead I would generalize in such as way, that i can pinpoint it anywhere. That is what you can consider the nth term

So we have to look at the behavior of the sequences, and see if we can generalize.

Most of the time you do so by listing numbers and looking for patterns.

a) 7, 49, 343, 2401,.....

If you look at those values we can see the following
7 = 7
49 = 7 * 7
343 = 7 * 7 * 7

So we can say that the nth term is 7^n when n >= 1 or n is an element of N

b)
4 , 12 , 20 , 28

That one has something developing
4 * 1 = 4
4 * 3 = 12
4 * 5 = 20
4 * 7 = 28
4 * (Odd number)
4 * (2n-1) where n is element of N

c)
That last one maybe we can see something here
2 ( 1) = 2
2 ( 3) = 6
2 ( 6) = 12
2 (10) = 20

1 = 1
1 + 2 = 3
1 + 2 + 3 = 6
1 + 2 + 3 + 4 = 10
That can be written as n*(n+1)/2
2 * ((n^2+n)/2)

Answer 3

The "n"th term in a series means that you replace the numbers with an expression that uses the variable "n". The first term in the series is generated when you let n=1. The second term is generated when you let n=2, and so on.

a)
The first term is 7^1, the second term is 7^2, the third term is 7^3. So, the nth term is 7^n. If you want to know the 100th term, you just let n=100.

b)
The first term is 4. The second term is larger by 8. The third term is again larger by 8. The fourth term is still larger by 8. So, the nth term is 8*n - 4. When n=1, you have 8 - 4 = 4. When n=2, you have 16 - 4 = 12, and so on.

c)
The first term is 1*2. The second term is 2*3. The third term is 3*4. The fourth term 4*5. So, the nth term is n*(n+1). When n=1, you have 1*2 = 2. When n=2, you have 2*3 = 6. When n=3, you have 3*4 = 12, and so on.

Answer 4

a. No. In the question, n is a variable, and what is required is an expression, presumably in terms of n, which gives the value for any particular term if n is given. In this case, each term is the preceding term multiplied by 7, and since the first term is 7, the nth term will be 7^n.
b. Each term is 8 more than its predecessor, so the general expression for the nth term is 8n-4.
c. The difference of adjoining terms increases by 2 with each term. That means that the difference of the differences is 2, and since this is a constant, the general expression will be a quadrilateral. Suppose that it is an^2 + bn + c. We have values of this for n = 1, 2, 3. and 4, so equations can be developed for a, b, and c and solved as a linear system to get the form of the general expression.

Answer 5

No, each term is got from the previous by multiplying by 7. So nth term is 7 raised to the n or 7^n. Try any n and it has to give you the right answer.

b) add 8 each time so 4 +8(n-1)

c) trrickier. 1squared +1, 2squared +2, 3 squared +3 so nth term is

n^2 + n