SOLUTION: Find the 10th term of the sequence -37,-34,-41

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Question 1197256: Find the 10th term of the sequence -37,-34,-41
Found 3 solutions by MathLover1, ikleyn, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Find the 10th term of the sequence
-37,-34,-41

nth term equation is:
a%5Bn%5D=an%5E2%2Bbn%2Bc

first term: -37 =>n=1
second term:+-34 =>n=2
third term: -41+=>n=3

make system of equations:
+-37=a%2A1%5E2%2Bb%2A1%2Bc
-34=a%2A2%5E2%2Bb%2A2%2Bc
-41=a%2A3%5E2%2Bb%2A3%2Bc
_____________________
++-37=a%2Bb%2Bc..........eq.1
-34=4a%2B2b%2Bc..........eq.2
-41=9a%2B3b%2Bc..........eq.3
_____________________
subtract eq.1 from eq.2
-34-%28-37%29=4a%2B2b%2Bc-a-b-c
3=3a%2Bb
b=3-3a..........eq.1a

subtract eq.1 from eq.3
-41-%28-37%29=9a%2B3b%2Bc-a-b-c
-4=8a+%2B+2b.....divide by 2
-2=4a+%2B+b
b=-2-4a.............eq.2a
from eq.1a and eq.2a we have
3-3a=-2-4a
4a-3a=-2-3
a=-5

go to
b=3-3a..........eq.1a, substitute a
b=3-3%28-5%29
b=3%2B15
b=18

go to

++-37=a%2Bb%2Bc..........eq.1, substitute a and b

++-37=-5%2B18%2Bc..........solve for c
++-37%2B5-18=c
c=-50
so, solving this system we got
a+=+-5, b+=+18, c+=+-50

then nth term equation is:
a%5Bn%5D=-5n%5E2%2B18n-50

now we can find the 10th term of the sequence

n=10
a%5B10%5D=-5%2A10%5E2%2B18%2A10-50
a%5B10%5D=-370




Answer by ikleyn(52795) About Me  (Show Source):
You can put this solution on YOUR website!
.

To get another, equally valid solution, I will assume that the sequence is cyclical and repeats itself infinitely many times.

Then the 10-th term is -37.


I specially presented here this example to show you (to convince you) that without having additional info
about the given sequence, the posed question makes no sense (is non-sensical, in other words).

Do not accept any other answer,  except of mine :   this question  MAKES  no  SENSE.

            DIAGNOSIS :


        The posed  " problem "  is  NONSENSE.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


As the response from tutor @ikleyn says, the problem is nonsense; there is no way to know what the subsequent terms of the sequence are. ANY following numbers make a valid sequence.

Tutor @MathLover1 assumes the sequence is quadratic and obtains a solution. It is true that, given a sequence of 3 terms, there is a unique polynomial function of degree 2 for which f(1), f(2), and f(3) are the three given numbers.

But the problem does not say that the sequence is quadratic; it is bad mathematics to assume it is. Furthermore, there are an infinite number of polynomials of degree greater than 2 which produce the given first three numbers.

A third "obvious" pattern is that the sequence of differences "plus 3, minus 7" repeats, giving the sequence

-37, -34, -41, -38, -45, -42, -49, -46, -53, -50

In that sequence, the "obvious" 10th term is -50.

So go with the answer from tutor @ikleyn: The problem as posed is nonsense.