Salary of Sharmila, when her salary is Rs. 5,00,000 for the first year and expected to receive yearly increase of 10% .

Question

In the following situation, does the list of numbers involved in the form a G.P.? 

Salary of Sharmila, when her salary is Rs. 5,00,000 for the first year and expected to receive yearly increase of 10% .

Answer 1

Given: Sharmila’s yearly salary = Rs. 5,00,000.

Rate of annual increment = 10 %.

Here, a = a₁ = 5,00,000 

a₂ = 5,00,000 × \(\frac{11}{10}\) = 5,50,000 

a₃ = 5,00,000 × \(\frac{11}{10}\) × \(\frac{11}{10}\) = 6,05,000 

a₄ = 5,00,000 × \(\frac{11}{10}\) × \(\frac{11}{10}\) × \(\frac{11}{10}\) = 6,65,000

Every term starting from the second can be obtained by multiplying its pre¬ceding term by a fixed number \(\frac{11}{10}\).

∴ r = common ratio = \(\frac{11}{10}\)

Hence the situation forms a G.P.