What's the nth term of this sequence?

Question

12, 27, 52, 87, 132...

And how do you work it out?
Thanks!

Apparently it's
"?n[squared] + ?

Answer 1

If it were a constant difference d between terms then it would be straightforward.

a(n) = a(0) + (n-1)d

This sequence is a bit more complicated because the difference between each number is itself an arithmetic sequence (15, 25, 35, 45, etc.). The next number should be 187 (132 + 55).

Let d be the starting number (15) in this sequence.
And let C be the difference *increase* in this new sequence (10).

Instead of the normal arithmetic sequence formula you want the changing difference formula:

a(n) = a(0) + (n-1)d + (C/2)(n-1)(n-2)

Where:
d = the first difference (15 in the sequence above).
C = The difference increase (10 in the sequence above).
a(0) = the first term (12)

a(n) = 12 + (n-1)15 + 5(n-1)(n-2)

Multiplying it all out:
a(n) = 12 + 15n - 15 + 5(n² -2n - n + 2)
a(n) = 12 + 15n - 15 + 5n² -15n + 10
a(n) = 5n² + 15n - 15n + 12 - 15 + 10
a(n) = 5n² + 7

Now let's double check the answer:
a(1) = 5(1)² + 7
a(1) = 5 + 7
a(1) = 12

a(2) = 5(2)² + 7
a(2) = 20 + 7
a(2) = 27

a(3) = 5(3)² + 7
a(3) = 45 + 7
a(3) = 52

a(4) = 5(4)² + 7
a(4) = 80 + 7
a(4) = 87

a(5) = 5(5)² + 7
a(5) = 125 + 7
a(5) = 132

a(6) = 5(6)² + 7
a(6) = 180 + 7
a(6) = 187

Therefore the answer is:
a(n) = 5n² + 7

Answer 2

To find the nth term in any sequence, the formula is
tn = a + (n-1)d where a- first number and d - constant difference..
There are 2 Arithmetic Progressions involved here..
in our case a1 = 12.
d1 = dn as the d is dynamic and vary

but the difference d follow a regular AP where you add 15 to the first, 25, 35 and so on...
so for this
so dn = 15 + (n-2)10 , as a2 = 15 and d2 = 10.
Here its n - 2 because the second AP starts only from second term of the first AP. So its nothing but
d(n-1) = 15 + (n-1-1)d = 15 + (n-2)d
so on combining the 2 APs together..
tn = 12 + (n-1)(15 + (n -2)10)
on simplifying..
tn = 12 + (n -1) (10n-5)

Answer 3

the nth number is 5n^2 + 7 ( i think)
as feed pointed out the differences between each number is 15 25 35 etc but the formula for that is not 10n - 5 but 10n + 5.

To get the nth number in your sequence you need to add up the numbers in feed's sequence up to n-1 and then add 12 to the result

sum of feed's sequence is
(Nth number + first number{15}) * N /2
ie
N = 3 SumFeed(((10 * 3 + 5) + 15) * 3) / 2 =75
N = 4 SumFeed(((10 * 4 + 5) + 15) * 4) / 2 = 120

SumFeed = (10N + 5 +15) N/2
=(10N^2 + 20N )/2 = 5N^2 + 10N

so nth number in sequence = SumFeed(n-1) +12
= 5(n-1)^2 + 10(n-1) +12
=5(n^2 -2n +1) + 10n -10 +12 = 5n^2 -10n +5 + 10n -10 +12
= 5n^2 +7 {I hope}

Answer 4

Let T(n) be the value of the nth term
Let n be the number of the term, where term 1 is 12

T(n) = T(n-1) + 5 + 10 X (n-1)

Answer 5

It is n squared, because you are creating a quadratic formula. basicly what you have to do is work out the 1st difference (the difference between the numbers). Which is 15,25,35,45. Now you work out the differences between those numbers (called the second difference): and it is 10,10,10,10. So now you need to use this formula: Nth term=a x n(squared) + b x n + c.
And now you need to work out a b and c. so you say n=1 which would be: a1+b1+c
then u say n=2: a4+b2+c
then u say n=3: a9+b3+c
And now you just have to work them out, the same way you work out simultaneous equations. Then you will have something nsquared + something + N + something.

Answer 6

Hey This sequence will not come in Arithmetic progression as its difference is not constant between a term and preceding term.And Geometric Progression, The ratio of a term and preceding term should be constant. but it is not G.P.and I think it will not come in Harmonic Progression. If u want to know how to find out nth term of Arithmetic Progression, Use a+(n-1)d and for Geometric Progression, Use Tn= arn-1 (this n-1 should come as exponential form i.e "ar raised to n-1") and for Harmonic Progression use 1/a+(n-1)d (this slash represent division)
I think you are genius.
Wish you good luck.

Answer 7

You're adding 15, 25, 35, 45...

So, if it's the second term, it's adding 15.
If it's the third term, it's 25.

So, for n, it would be 10n-5.

Btw, please:
http://answers.yahoo.com/question/index;_ylt=AlNDuhHIje3a7cAWfwUPFM_sy6IX;_ylv=3?qid=20071110183049AALG9cw

n squared?
How is it n squared? O_O

It can't be... 12^2 = 144... how can that reach the second term which is 27?

Answer 8

you have to notice that the difference of the difference between them is 10 and take it from there. i forgot exactly how.

15, 25, 35, 45...
difference between these is 10...
I know you do something like this but I forgot.