Growth Problem

auspicious

Initial value is 10
There are 50 periods.
In the first period, 10 is the added value.
Each successive period, the added value increases by 10

period 1 is 10 + 10 = 20
period 2 20 + 20 = 40
3. 40 + 30 = 70
4. 70 + 40 = 110

What is the final figure after 50 periods?

Horusire

auspicious wrote: »

Initial value is 10
There are 50 periods.
In the first period, 10 is the added value.
Each successive period, the added value increases by 10

period 1 is 10 + 10 = 20
period 2 20 + 20 = 40
3. 40 + 30 = 70
4. 70 + 40 = 110

What is the final figure after 50 periods?

Is this the 49th term in the fibonacci sequence with an added zero?

auspicious

It's not homework. It's something I've been pondering over the past hour or so.
And I think the fibonacci sequence does not work here.
Surely there is an equation.
Or is it just a matter of laborious addition?

Thanks.

MathsManiac

You could do it by laborious addition, but there is a better way.

Note the following:

The thing you're adding on each time is increasing by a fixed amount. That means that the sequence of things you're adding on is an arithmetic sequence.

Look up arithmetic sequence, and, particular, sum to n terms of an arithmetic sequence, and you should be able to work it out. Come back if you need more help.

auspicious

g (n) = 5n^2 +5n + 10

Input:
Table[5 n^2 + 5 n + 10, {n, 1, 50}]

Result
{20, 40, 70, 110, 160, 220, 290, 370, 460, 560, 670, 790, 920, 1060, 1210, 1370, 1540, 1720, 1910, 2110, 2320, 2540, 2770, 3010, 3260, 3520, 3790, 4070, 4360, 4660, 4970, 5290, 5620, 5960, 6310, 6670, 7040, 7420, 7810, 8210, 8620, 9040, 9470, 9910, 10360, 10820, 11290, 11770, 12260, 12760}