anonymous one year ago I know I'm just overthinking this and it's literally probably an x=y formula but humor me. Midas wants to buy all the land near his house. There are 65 lots surrounding his home, and each lot costs \$7200. But for every lot purchased, the price doubles. How much money does Midas need to buy all 65 lots?

1. arindameducationusc

Use sum of GP series here

2. arindameducationusc

a(R^n-1) / R-1 here a= 7200 n=65 and r=2

3. nincompoop

it says for every lot purchased, the price doubles you can try without the fancy geometric series by using simple arithmetic first Price per lot = 7200 number of lots 65 normally it would be 65* 7200 but the condition is that the price increases for every additional lot purchased so if we start with the first lot $$L_1 = 7200$$ then second lot $$L_2 = 2 \times L_1$$ then third $$L_3 = 2 \times L_2$$ we can quickly see that we are doubling the previous price

4. nincompoop

so maybe it would be safe to say that our addition of lot sequence would be $$\large L_1 + L_2 + L_3 ... L_{65}$$ we will worry about inserting each of $$L_n$$ prices later and focus on how we can write L into condensed form. Have you done any summations in the past?

5. nincompoop

humour me

6. Kainui

Let's pretend for a second there are only 3 lots. Then the prices for buying will be: $7200 + 2*7200+ 2*2*7200$ Which simplifies to $7200(1+2+4)$ So this is where the geometric series comes in, instead of only having 3, we have 65 which will be a geometric series in 2 which is exactly what @arindameducationusc is referring to here.

7. arindameducationusc

Nice @Kainui & @nincompoop... Good job!