A worker is supposed to dig a well 37m deep. He charges 1 euro cent for the first meter, but then the price is to be increased by 50% from meter to meter. The client agrees to this. What amount does he have to pay?

asinus Jun 26, 2021

#1**+3 **

**"He charges 1 euro cent for the first meter, but then the price is to be increased by 50% from meter to meter."**

Let's take this into account as an GP such that

GP = 1, 1.5, 2.25,... and so on

⇒ a = 1 and r = 1.5

Length of the well is 37 m i.e. the no. of terms in the GP is 37.

Now, in order to calculate the total amount, we find the sum of 37 terms in the GP

∵ \({S}_{n}={a(r^n-1)\over r-1}\)

⇒ \({S}_{37} = {1((1.5)^{37}-1)\over 1.5-1} ≈ 6552491.2\)

Thus he has to pay **6,552,491.2 euro cents**.

amygdaleon305 Jun 26, 2021

#1**+3 **

Best Answer

**"He charges 1 euro cent for the first meter, but then the price is to be increased by 50% from meter to meter."**

Let's take this into account as an GP such that

GP = 1, 1.5, 2.25,... and so on

⇒ a = 1 and r = 1.5

Length of the well is 37 m i.e. the no. of terms in the GP is 37.

Now, in order to calculate the total amount, we find the sum of 37 terms in the GP

∵ \({S}_{n}={a(r^n-1)\over r-1}\)

⇒ \({S}_{37} = {1((1.5)^{37}-1)\over 1.5-1} ≈ 6552491.2\)

Thus he has to pay **6,552,491.2 euro cents**.

amygdaleon305 Jun 26, 2021