(Q15).In which of the following situations, does the list of numbers involved in the form a G.P.?

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

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

Rate of annual increment = 10%.

Year 01 02 03 04
Salary

500000

a

500000(1+
10
100
 )

a.r

500000(1+
10
100
 )2

a.r2

500000(1+
10
100
 )3

a.r3

Here, a = a1 = 5,00,000

a2 = 5,00,000 ×
=
a3 = 5,00,000 ×
×
=
a4 = 5,00,000 ×
×
×
=
Clearly,
a2
a1
 =
500000 ×
500000
 =
a3
a2
 =
500000 ×
×
500000 ×
=
Clearly,
a4
a3
 =
500000 × (
)3
500000 × (
)2
 =
11
10
Every term starting from the second can be obtained by multiplying its preceding term by a fixed number
∴ r = common ratio =

Hence the situation forms a G.P.