Question

A tube well is dug 800 meters deep. The 1st meter costs $110 to dig and the cost per meter increases by $35 for every subsequent meter. Find the cost of digging the 500th meter AND the total cost incurred for the entire job.

Answer 1

(a)$17,575.

(b)$11,274,000

Step-by-step explanation:

Length of the tube well =800 meters

Cost of the 1st meter = $110

The cost per meter increases by $35 for every subsequent meter.

We can model this problem as an arithmetic progression where:

• First term, a = $110

,

• The common difference, d =$35

(a)The cost of digging the 500th meter

The nth term of an arithmetic progression is derived using the formula:

`U_n=a+(n-1)d`

Therefore, the 500th term will be:

`\begin{gathered} U_(500)=110+35(500-1) \\ =110+35*499 \\ =110+17465 \\ =\$17,575 \end{gathered}`

The cost of digging the 500th meter is $17,575.

(b)The total cost incurred will be the cost of digging 800 meters of the tube well.

We obtain this by finding the sum of the cost for each meter.

The sum of an A.P. can be obtained using the formula below:

`S_n=(n)/(2)\mleft(2a+(n-1)d\mright)`

Substitution of the given values, we have:

`\begin{gathered} S_(800)=(800)/(2)(2*110+(800-1)35) \\ =400(220+799*35) \\ =400(220+27965) \\ =400*28185 \\ =\$11,274,000 \end{gathered}`

The total cost incurred for the entire job is $11,274,000.