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
Yes. You can have as many nth terms as you can be bothered to write down!
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
The Nth partial sum is the sum of the first n terms in an infinite series.
It means to work out a suitable nth term that is applicable to all terms of a sequence of numbers following a regular pattern.
5 first terms in n²+3
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.
2,1,0 is th sequence of its terms
no clue
They are: 6 15 24 33 and 42
3,6,9,12,.. 7,14,21,28,.. -2,-4,-6,-8,... 5,9,13,17 3,8,13,18
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.
29