SOLUTION: 1. The nth term of a sequence is given by the formula: n/2(3n^2+1), find the 6th terms. 2. The nth term of a sequence is denoted by 3n(2^n-1), find the sum of the first 5 terms

Algebra ->  Sequences-and-series -> SOLUTION: 1. The nth term of a sequence is given by the formula: n/2(3n^2+1), find the 6th terms. 2. The nth term of a sequence is denoted by 3n(2^n-1), find the sum of the first 5 terms       Log On


   

Question 1122533: 1. The nth term of a sequence is given by the formula: n/2(3n^2+1), find the 6th terms.
2. The nth term of a sequence is denoted by 3n(2^n-1), find the sum of the first 5 terms
3. What is the value of X for which the expression is not defined: 2x+3/x2-16?
Found 3 solutions by mananth, greenestamps, Edwin McCravy:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
1. The nth term of a sequence is given by the formula: n/2(3n^2+1), find the 6th term.
a%28n%29+=+%28n%2F2%29%283n%5E2%2B1%29
a%286%29+=+%286%2F2%29%283%2A6%5E2%2B1%29
a%286%29+=+3%2A%283%2A36%2B1%29
a%286%29+=+3%2A109%29
a(6) = 327
2. The nth term of a sequence is denoted by 3n(2^n-1), find the sum of the first 5 terms
a(n) =3n(2^n-1)
a(1) = 3
a(2)= 18
a(3)= 63
a(4)=180
a(5)= 465
Add them up
3. What is the value of X for which the expression is not defined: 2x+3/x2-16?

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


About the third question, which the other tutor didn't address in her response....

The real response to that question is that "X" does not appear in the given expression "2x+3/x2-16", so the question makes no sense.

In working a problem using algebra, X and x can represent two different numbers.

If we assume X and x are supposed to be the same number, then the answer to the question is not what you were expecting.

"2x+3/x2-16" --> 2x%2B3%2Fx2-16

In that expression, the expression is not defined when the denominator of the fraction is 0, which is when x=0.

ANSWER: 0

But that is undoubtedly not the answer you were looking for, because you didn't show the expression correctly.

The careful use of parentheses is important in algebra. It's almost certain that the expression you wanted is "(2x+3)/(x2-16)" --> %282x%2B3%29%2F%28x2-16%29.

Of course the answer to that question is completely different.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Greenestamps beat me to it. 
3. What is the value of X for which the expression is not defined: 2x^""+3/x^2-16?

I'm always suspicious when I see an expression like this with no parentheses.

If you mean what you wrote, which I doubt (from experience with students)

2x%2B3%5E%22%22%2Fx%5E2-16 is undefined when x = 0.

If you meant this 

%282x%2B3%5E%22%22%29%2Fx%5E2-16 is undefined when x = 0.

If you meant this:

2x%2B3%5E%22%22%2F%28x%5E2-16%29 is undefined when x%5E2-16=0

That is, when %28x-4%29%28x%2B4%29=0}, or x = 4 or x = -4.

%282x%2B3%5E%22%22%29%2F%28x%5E2-16%29 is undefined when x%5E2-16=0

That is, when %28x-4%29%28x%2B4%29=0, or x = 4 or x = -4.

When you type math all on one line, you must always put parentheses
around numerators and denominators.  All of the above mean different 
things.

Edwin