Question

The fees for the first three years of a hunting club membership are given in Table 1. If fees continue to rise at the same rate, how much will the total cost be for the first ten years of membership? 

Answer 1

Consider the fees for the first three years of a hunting club membership,

$1500, $1950, $2535

 

Find the ratio of second term to the first term,

a2 ÷ a1 = 1950 ÷ 1500

             = 1.3

 

Find the ratio of second term to the third term,

a3 ÷ a2 = 2535 ÷ 1950

             = 1.3

 

As two ratios are equal, the given terms make a geometric sequence.

First term is, a1 = 1500

And, common ratio is, r = 1.3

 

Use the formula for the sum of first n terms of a geometric sequence,

Sn = a1∙(1 – rn)/(1 – r) ...... (1)

 

Substitute a1 = 1500, r = 1.3 and n = 10 in the formula (1) and simplify,

S10 = 1500 × (1 – 1.310)/(1 – 1.3)

        = 1500 × (1 – 13.7856491849)/(-0.3)

       = 63929.2459245

 

Rounding to two decimal places,

S10 = 63,929.25

 

Therefore, the total cost for the first 10 years of membership will be $63,929.25.

Therefore, the total cost for the first 10 years of membership will be $63,929.25.