SOLUTION: What is the nth term of the sequence 20 27 32 35 36

Algebra.Com
Question 1177145: What is the nth term of the sequence 20 27 32 35 36
Answer by greenestamps(13206)   (Show Source): You can put this solution on YOUR website!


Technically, the problem as stated is invalid; ANY next number would form a valid sequence.

However, there is a clear pattern in the numbers shown: the differences between successive term from an arithmetic sequence.

That means the differences between those differences (mathematically, the second differences of the given sequence) are constant; in fact they are all -2.

We can display all of this in an array like this:
   20  27  32  35  36  the given terms of the sequence
      7   5   3   1    the first differences
       -2  -2  -2      the second differences

A constant second difference means the sequence can be formed by a polynomial of degree 2:



Use that general quadratic equation with the fact that t(1)=20, t(2)=27, and t(3)=32 to write and solve a system of three equations in a, b, and c.

That will give you what you are looking for -- a quadratic equation that determines the n-th term in the sequence.


RELATED QUESTIONS

the third term of a geometric sequence is 4 and the sixth term is 32/27. find the nth... (answered by MathLover1)
What is the 5th term of this sequence? What is the nth term of this sequence? 8, 12, (answered by nerdybill)
What is the nth term of the sequence:... (answered by ikleyn)
what is the nth term of the sequence... (answered by MathLover1)
Find a formula for the nth term of the arithmetic sequence: 32, 36, 40, 44,... (answered by nyc_function)
what is the nth term of the sequence... (answered by richwmiller)
what is the nth term of the sequence... (answered by Edwin McCravy)
What is the nth term of arithmetic sequence... (answered by solver91311)
What is the nth term of this number sequence... (answered by josgarithmetic)