sequences

[yfelix45]

Hello good morning,

I am stuck on this question.
This sequence: 0, 3, 8, 15, 24,35, 48, 65 are the first eight terms.

a) write the function f(x) that would correspond to this sequence.
my ans: x^2 +1


b) Write the general term t^n (an equation ) for the n th term of this sequence.
my ans: t^n = x^2 + 1

c) write a recursive formula forthis sequence.

d) Find the 13th term of this sequence using the formula from a).

When I use the formula from a) my ans = t^13 = x^2 +1
= (13)^2 +1
= 169 +1
= 170.


If I count the sequence as I have,(0+3 =3, 3+5 = 8,8+7=15, 15+ 9=24,24+11= 35,.........) The answer would be completely different to the one using the formula.

Can you explain how to find the term of a sequence and write a recursive formula when the values used in the sequence are different?

Thanks
yfelix45

 

[biffboy]

Sequences

Apart from the 65 those terms fit n^2-1 Should that last term have been 63?

 

[TchrWill]

Hello good morning,

I am stuck on this question.
This sequence: 0, 3, 8, 15, 24,35, 48, 65 are the first eight terms.

a) write the function f(x) that would correspond to this sequence.
my ans: x^2 +1


b) Write the general term t^n (an equation ) for the n th term of this sequence.
my ans: t^n = x^2 + 1

c) write a recursive formula forthis sequence.

d) Find the 13th term of this sequence using the formula from a).

When I use the formula from a) my ans = t^13 = x^2 +1
= (13)^2 +1
= 169 +1
= 170.
If I count the sequence as I have,(0+3 =3, 3+5 = 8,8+7=15, 15+ 9=24,24+11= 35,.........) The answer would be completely different to the one using the formula.
Can you explain how to find the term of a sequence and write a recursive formula when the values used in the sequence are different?

n...............1....2....3....4....5....6....7....8
N...............0....3....8...15..24...35..48..63
1st Diff...........3....5....7....9...11...13..15
2nd DIff.............2....2....2....2....2....2

Being a finite difference series with second differences constant, the general expression for the nth term is of the form N = an^2 + bn + c. Using the data generated above:

a(1)^1) + b(1) + c = 0 or a + b + c = 0 (1)
a(2^2) + b(2) + c = 3 or 4a + 2b + c = 3 (2)
a(3^2) + b(3) + c = 8 or 9a + 3b + c = 8 (3)

Subtracting 1 from 2 and 2 from 3 yields
3a + b = 3
5a + b = 5

Subtracting
2a = 2 making a = 1, b = 0 and c = -1 resulting in N = n^2 - 1

The 13th term is therefore 13^2 - 1 = 168.

 

[yfelix45]

Thanks

Hello,

A great thanks to biffboy and TchrWill for helping me with my question and things much more clearer!!!

THANKS!!!!!!!!

yfelix45