A 30 meter borehole is to be drilled. The cost of drilling is $20 for the first meter, and the cost for drilling each additional meter is $3 more than that of the preceding meter.

Question

(a) What is the drilling cost for the 30 meter deep borehole?

(b) If you have only $1000 available, how deep a borehole can you afford?

Answer 1

cost

= 20+23+26+29+ .. a30

where each term is 3 more than previous term

an AP with d=3, a1=20

an =a1 +d(n-1) = 20 +3(n-1) = 3n+17

a30 = 3(29)+17 = 87+17=$104 for 30th meter

sn = n(a1+an)/2 = 30(20+104)/2 = 15(124) =$1995 = cost of 30 meter hole

with only $1,000 budget the most that can be dug is 20 meters

20+23 + ... +74+ 77 = $970. another meter costs over budget

an=77

sn=(n/2)(20+77)= (97n)/2=48.5n </=1,000

n =/< 1000/48.5=about 20.6

20th term/meter

20 meters maximum on $1,000 budget