# math

posted by .

0,4,18,48,100.....

How can I find the general term for this ?

• math -

I found that the third differences were a constant of 6, so we have a cubic.

assume the function is
f(x) = ax^3 + bx^2 + cx + d

for (1,0) --> a + b + c + d = 0 ..... #1
for (2,4) --> 8a + 4b + 2c + d = 4 ....#2
for (3,18) -> 27a + 9b + 3c + d = 18 .. #3
for (4,48) -> 64a + 16b + 4c + d = 48 ... #4

#2 - #1 --> 7a + 3b + c = 4 .....#5
#3 - #2 --> 19a + 5b + c = 14 ....#6
#4 - #3 --> 37a + 7b + c = 30 ....#7

#6 - #5 ---> 12a + 2b = 10 ----> 6a + b = 5
#7 - #6 ---> 18a + 2b = 16 ----> 9a + b = 8

subtract these last two:
3a = 3
a = 1

in 6a + b = 5 ---> 6+b=5 , ---- b = -1

in #5: 7a + 3b + c = 4
7 - 3 + c = 4 ------------- c = 0

in #1:
a + b + c + d = 0
1 - 1 + 0 + d = 0
d = 0

so our general term is
x^3 - x^2

or
term(n) = n^3 - n^
= n^2 (n-1) , where n ∈ N

testing:
term(1) = 1^3 - 1^2 = 0
term(2) = 2^3 - 2^2 = 4
term(3) = 3^3 - 3^2 = 27-9 = 18
term(4) = 4^3 - 4^2 = 64-16 = 48
term(5) = 5^3 - 5^2 = 125 - 25 = 100

## Similar Questions

1. ### math+ check!

the following sequence is geometric: 4/3, 4/9, 4/27.... determine the general term, tn and the term t10 so the general term is: (4/3)x (1/3) ^n so the tenth term is: 4/177147 is this correct?
2. ### math

the "k"th term of a series, Sk=a 1-r^k/1-r, is the sum of the first "k" terms of the underlying sequence. the difference between the "n"th terms of two particular series is greater than 14 for some values of n (is an element of) N. …
3. ### MATH

In an arithmetic sequence, the first term is 100 and the sixth term is 85. Find the common difference. Then, find the 50th term of the sequence. Do I use the formula an=a1+(n-1)d?
4. ### Math ( Can You check my Work?)

1.an = 3n - 1 2. an = 2(2n - 3) 3.an = 4^n 4.an = (2/3)^n 5. an = (-1)^n(n + 5) 6. an = (-1)^n + 1(n + 6) 7. an= n+3/2n-1 8. a1 = -5 and an = an-1 - 3 for n ≥ 2 9. a1 = -6 and an = -2an-1 for n ≥ 2 10.a1 = 4 and an = 3an-1 …
5. ### Math SL

An Arithmetic sequence has a tenth term of 17 and a fourteenth term of 30, ind the general term PLEASE HELP!!!!
6. ### Math

make a table of values for the sequence 6,11,16,21,26 b) write an algebraic expression for the general term of the sequence. c) Use ur expression for the general term to calculate the 25th term in the sequence. Please help asap
7. ### maths

The 2nd term in Geometric sequence is -4 and the 5th is 32 ,find the general formula \term and the first 3 terms ,find the 18th term
8. ### Math binomial formula and sequence

a) use the binomial formula to find the 5th term of the expansion (2x - 3)^8 ------ i got 90720x?
9. ### MATH_2016

For the geometric sequence, -100,50,-25,12.5, find the next two terms and the general term.
10. ### math

Given that the sum of the first 20 terms of an arithmetic sequence is 1150 and the fifth term is twice the second term . find: 1.The first term and the common difference 2. find the general formula

More Similar Questions