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Ten new graduates of IT are employed by the leading telecommunication company in January 2016.  Their employment contract has a provision that after 6 months if they meet the requirements and performance level expected from them, they will be become regular employees and enjoy the perks and benefits given to regular employees.  

Also after six months and every six succeeding months, their basic salary will be increased by 1.10 times. 

So if x is the basic salary upon employment, it is the first term, a₁.  What will be the salary after 6 months?  after 12 months?

Let's say the basic salary upon employment is Php 10,000.

a₁ =salary upon employment, Php10,000
a₂ = salary after six months
a₃ = salary after 12 months
d = 1.10

General Formula:    a_{n}  = a₁  (r)^{n-1}

After 6 months, n=2:
a₂ = 10,000 (1.1)^{2-1}
a₂ = 10,000 (1.10)¹
a₂ = 11,000  (Salary after 6 months)

After 12 months, n=3:
a₃ = 10,000 (1.1)³⁻¹
a₃ = 10,000 (1.10)²
a₃ = 10,000 (1.21)
a₃ =  12,100  (salary after 12 months)

To write the salaries in sequence:

10,000,   11,000,   12,100

Why is it a geometric sequence? Check if the ratio is common.
11,000 ÷ 10,000 = 1.1
12,000 ÷ 11,000 = 1.1

Have a great day :-)

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