Here are the first four terms of a sequence.
4, 11, 22, 37
Find an expression, in terms of n, for the nth term of this sequence.
Answers
Answer:
2n² + n + 1
Step-by-step explanation:
I'll admit, I had to look this one up but I could only find the answer. I had already found 2n² because...
4, 11, 22, 37
Difference between: 7, 11, 15
7,11,15 are all 4 apart. You divide the 4 by 2 to get 2n² (it is squared because you needed a second level to find the difference)
And then I knew you needed to put the original 2n² with the sequence we are trying to work out.
2, 8, 18, 32
4, 11, 22, 37
difference between the 2 sequences 2, 3 ,4 ,5 (which all has a difference of 1) which means 1n or just n.
So that's 2n² + n
I really want to know where the + 1 comes from though!
Given:
The first four terms of a sequence are 4, 11, 22, 37.
To Find:
The nth term of the given sequence.
Solution:
1. The given sequence is 4, 11, 22, and 37.
2. The first term can also be written as,
= > 4 = 2 x 1^2 + 1 + 1,
3. The second term can also be written as,
= > 11 = 2 x 2^2 + 2 + 1,
4. The third term can also be written as,
= > 22 = 2 x 3^2 + 3 + 1,
5. The fourth term can also be written as,
= > 37 = 2 x 4^2 + 4 + 1,
6. The general sequence is (2 x n^2 + n + 1), The fifth term of the sequence is,
= > Fifth term = 2 x 25 + 5 + 1 = 56.
Therefore, the nth term of the sequence is 2 x n^2 + n + 1.