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.Com
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) (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 = 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)
RELATED QUESTIONS
the nth term of a sequence is (n-2)/n^2 write the first three terms of this... (answered by stanbon)
the nth term of a different sequence is n-2/n2 write the first three terms of this... (answered by venugopalramana)
Here are the first five terms of a sequence:
2,2,0,,-4,-10
An expression for the nth... (answered by MathLover1)
The Nth Term Of Sequence Is given by T(n) = 30-4n Generate the first 4 terms of the... (answered by ikleyn)
Write the first six terms of the sequence whose nth term is given as;
a^n = (-1)n / (answered by stanbon)
The nth term of a sequence is n²-n-2. Find the first 4 terms and the term which equals... (answered by josgarithmetic)
write the first five terms of the sequence in which the nth term is... (answered by Edwin McCravy)
Write the first five terms of the sequence in which the nth term is... (answered by amarjeeth123)
Write the first five terms of the sequence whose general term is... (answered by Fombitz)