Quick math-nerd question, probably pretty basic

[Howie Roary]

how do I calculate the sum total of a string of numbers starting at 2,700,000 (1 unit) which increase 10% (270,000) on each additional unit, and add each successive number, of which there are a total of 32,767 units or consecutive numbers

so:

1. 2,700,000
2. 2,970,000
3. 3,240,000
...
32767. 8,849,520,000


a formula would be helpful, as I also am wondering the total sum of:

1. 120,000
2. 132,000
3, 144,000
...
32767. 393,312,000


do I simply add the first and last numbers, divide them by 2 and multiply them by the total number of units (32767)

[RKenshin]

A bit unsure, but are you looking for an interest calculation? Sounds sort of like what you described.

In which case the sum (future value) is found through the following equation:

FV = PV*(1+i)^n

Where:
FV = Future Value (sum)
PV = Present Value (2,700,000)
i = Interest Rate (10%)
n = Number of Periods (32767)

So for your example, it would be:

FV = 2700000 * (1 + 0.1)^(32767)

Or wait, that can't be what you're looking for... as that number would be obscenely large. Correct if wrong?

[Howie Roary]

truthfully it's for a phone game called Vampires Live, and I want to know how much it will cost to purchase all of one particular defense unit, of which you can buy a max of 32767, and increases in cost as I've described, to the maximum number listed for the final unit

[SDSD]

how do I calculate the sum total of a string of numbers starting at 2,700,000 (1 unit) which increase 10% (270,000) on each additional unit, and add each successive number, of which there are a total of 32,767 units or consecutive numbers

so:

1. 2,700,000
2. 2,970,000
3. 3,240,000
...
32767. 8,849,520,000


a formula would be helpful, as I also am wondering the total sum of:

1. 120,000
2. 132,000
3, 144,000
...
32767. 393,312,000


do I simply add the first and last numbers, divide them by 2 and multiply them by the total number of units (32767)

Is this 10% increase a fixed 10% increase of the number your series starts at? From what I'm reading, it seems Series 1 increased by 270,000 each additional term in the series (10% of 2.7 million). Do you mean that essentially starting at 2.7 million, add a fixed constant, 270,000, toeach new term, up to 32767 terms?

Or do you really mean, when you refer to a an additional 10% increase on each new term in the series, as a 10% increase over the preceding term? So then you'd add 270,000 to the first term giving you 2,970,000, and then adding 297,000 to 2,970,000 for the next term in the series (which would then be 3,267,000 vs. 3,240,000 as with the fixed constant addition)?

The same question applies to the second problem you asked about.

[SDSD]

This formula should give you the answer to the first question where n=32767 or however many terms you want in the series. Adapt as needed for the second question. This is based on adding a fixed amount to each term (270,000 or 10% of the starting term).

[Waef]

Alright, gonna give this a shot here, and if it's horribly wrong, someone correct me please.

Let S1 = 2,700,000 + 2,970,000 + ... + 8,849,520,000
Let S2 = 8,849,520,000 + ... + 2,970,000 + 2,700,000

Now take S1+ S2 = (8,849,520,000 + 2,700,000) + ... + (2,700,000 + 8,849,520,000).

Then S1 + S2 = 8,852,220,000 + 8,852,220,000 + ... + 8,852,220,000, which is equal to 8,852,220,000 * 32767. Now, S1 + S2 is exactly twice the value of S1 on its own, so we must divide by 2.

Thus we have (32767*8,852,220,000)/2. Plug that into a calculator.

Edit: 145,030,346,370,000

1. 120,000
2. 132,000
3, 144,000
...
32767. 393,312,000


do I simply add the first and last numbers, divide them by 2 and multiply them by the total number of units (32767)

Yeah, I believe so.

[Howie Roary]

Is this 10% increase a fixed 10% increase of the number your series starts at? From what I'm reading, it seems Series 1 increased by 270,000 each additional term in the series (10% of 2.7 million). Do you mean that essentially starting at 2.7 million, add a fixed constant, 270,000, toeach new term, up to 32767 terms?

Or do you really mean, when you refer to a an additional 10% increase on each new term in the series, as a 10% increase over the preceding term? So then you'd add 270,000 to the first term giving you 2,970,000, and then adding 297,000 to 2,970,000 for the next term in the series (which would then be 3,267,000 vs. 3,240,000 as with the fixed constant addition)?

The same question applies to the second problem you asked about.

it's a fixed 270,000 added to each number. The 10% was only a 10% increase of the first number, with each subsequent number being the previous number + 270,000

[Tajin]

Already answered but could've used a spreadsheet software to get the sum done. obv. using the formula is faster.