SOLUTION: 1) Use the explicit formula an=(-1)^n(13n-6), to find the first five terms of the sequence. 2) Find the first five terms of the sequence given the following recursive formula: a1

Algebra ->  Sequences-and-series -> SOLUTION: 1) Use the explicit formula an=(-1)^n(13n-6), to find the first five terms of the sequence. 2) Find the first five terms of the sequence given the following recursive formula: a1      Log On


   

Question 1085370: 1) Use the explicit formula an=(-1)^n(13n-6), to find the first five terms of the sequence.
2) Find the first five terms of the sequence given the following recursive formula: a1=-3, a2=-7, and an=an-2an-1 for n_> 3.
3) Find the 34th term of this sequence: -35,-49,-63,-77,...
4) What is the 17th term in the arithmetic sequence in which a6 is 101 and a9 is 83?
Answer by ikleyn(52900) About Me  (Show Source):
You can put this solution on YOUR website!
.
1) Use the explicit formula an=(-1)^n(13n-6), to find the first five terms of the sequence.
2) Find the first five terms of the sequence given the following recursive formula: a1=-3, a2=-7, and an=an-2an-1 for n_> 3.
3) Find the 34th term of this sequence: -35,-49,-63,-77,...
4) What is the 17th term in the arithmetic sequence in which a6 is 101 and a9 is 83?
~~~~~~~~~~~~~~ 

1)  This problem is REMARKABLE.

    It is remarkable, because you do not need to think to solve it.

    You need simply plug in the numbers into the formula a%5Bn%5D = %28-1%29%5En%2A%2813n-6%29.

    For example, the first term  (n=1)  is  a%5B1%5D = %28-1%29%5E1%2A%2813%2A1-6%29 = -(13-6) = -7;


    The second term  (n= 2)  is   a%5B2%5D = %28-1%29%5E2%2A%2813%2A2-6%29 = 1*(26-6) = 20.


    AND SO ON . . .    Can you complete it on your own ??



2)  This problem is REMARKABLE too.

    It is remarkable due to the same reason: you do not need to think to solve it.

    You need simply plug in the numbers into the formula a%5Bn%5D = a%5Bn-2%5D%2Aa%5Bn-1%5D for n >= 3.

    
    For example, a%5B3%5D = a%5B1%5D%2Aa%5B2%5D = (-3)*(-7) = 21.

                 a%5B4%5D = a%5B2%5D%2Aa%5B3%5D = (-7)*(21) = -147,


    AND SO ON . . .  Can you complete it on your own ??