0
What is the n^th terms of 6,11,18,27,38
To find the nth term of the sequence 6, 11, 18, 27, 38, we can use the method of finite differences.
First, we calculate the differences between consecutive terms:
11 - 6 = 5 18 - 11 = 7 27 - 18 = 9 38 - 27 = 11
We can see that the second differences are all equal to 2. This tells us that the nth term is a quadratic function of n.
Next, we calculate the first differences between consecutive second differences:
7 - 5 = 2 9 - 7 = 2 11 - 9 = 2
Since the first differences between the second differences are all equal to 2, this tells us that the quadratic function is of the form:
an^2 + bn + c
where a = 1/2, since the second differences are all equal to 2.
To find the values of b and c, we can use the first two terms of the sequence:
When n = 1, the term is 6, so: a + b + c = 6
When n = 2, the term is 11, so: 4a + 2b + c = 11
Solving these two equations simultaneously, we get: b = 5/2 c = 3
Therefore, the nth term of the sequence is given by: an^2 + (5/2)n + 3/2
To find the nth term, we simply substitute the value of n into this formula. For example, to find the 6th term:
a(6)^2 + (5/2)(6) + 3/2 = 6(1/2)(36) + 15 + 3/2 = 18 + 15 + 3/2 = 36.5
Therefore, the 6th term of the sequence is 36.5.
Nili smith
Add your answer:
Earn +20 pts
Does a nth term go on forever?
Yes. You can have as many nth terms as you can be bothered to write down!
What are the first 4 terms of the sequence which has the nth term formula?
the first 4 terms of the sequence which has the nth term is a sequence of numbers that that goe together eg. 8,12,16,20,24 the nth term would be 4n+4
How do you find the nth partial sum?
The Nth partial sum is the sum of the first n terms in an infinite series.
What is the definition of finding the nth term?
It means to work out a suitable nth term that is applicable to all terms of a sequence of numbers following a regular pattern.
The nth term for n²-1?
5 first terms in n²+3
Are all patterns recursive?
No, patterns with terms that are not based upon previous terms are not recursive. Example: i * i where i is the nth term of the pattern.
What are the first five terms of the sequence whose nth term is N4 plus 225?
2,1,0 is th sequence of its terms
What are the first five terms of the sequence with nth term is 7n + 3?
no clue
What is the first 5 nth terms of 9n-3?
They are: 6 15 24 33 and 42
What is the first 5 terms in a sequence when given the nth term n 7?
3,6,9,12,.. 7,14,21,28,.. -2,-4,-6,-8,... 5,9,13,17 3,8,13,18
What is the sum of first six terms of a sequence whose nth term is 8 - n?
nth term is 8 - n. an = 8 - n, so the sequence is {7, 6, 5, 4, 3, 2,...} (this is a decreasing sequence since the successor term is smaller than the nth term). So, the sum of first six terms of the sequence is 27.
What is the first five nth terms of 34 - 5n?
29
