SOLUTION: The question is: The nth term of a sequence is 4/n^2 (a)Write down the first three terms of the sequence, expressing each term in its simplest form. (b)The kth term in the se

Algebra ->  Square-cubic-other-roots -> SOLUTION: The question is: The nth term of a sequence is 4/n^2 (a)Write down the first three terms of the sequence, expressing each term in its simplest form. (b)The kth term in the se      Log On


   

Question 309476: The question is:
The nth term of a sequence is 4/n^2
(a)Write down the first three terms of the sequence, expressing each term in its simplest form.
(b)The kth term in the sequence is 1/100
Find the value of k
Note: it is K not N
(c)Given that the nth term of the sequence is less than 0.0064, find the smallest value of n. '
I shall be highly glad if you help me.
Regards,
Benjamin.
Answer by alicealc(293) About Me  (Show Source):
You can put this solution on YOUR website!
(a)
n = 1 -> 4/1^2 = 4/1 = 4
n = 2 -> 4/2^2 = 4/4 = 1
n = 3 -> 4/3^2 = 4/9

(b)
n = k -> 4/k^2 = 1/100
4*100 = k^2
400 = k^2
k+=+sqrt%28400%29
k = 20

(c)
4/n^2 < 0.0064
4/0.0064 < n^2
625 < n^2
0 < n^2 - 625
0 < (n - 25)*(n + 25)
n = 25 or n = -25
++ -- ++
--o--o---
-25 25
*if n = 0 then 0^2 - 625 = -625 -> it gives the negative result for n = 0
because n = 0 is between -25 and 25, so the area between -25 and 25 will give negative result for the equation, and the left side and the right side of that area will give positive result
*because the equation should make result that is greater than 0 (>0) so the solution set for that inequality is the area that gives positive result.
so, n < -25 or n > 25

because n should not be negative number, the smallest value of n so that the nth term of the sequence is less than 0.0064 is 26 (the first integer that is greater than 25)