Question

In which of the following situations, does the list of numbers involved in form a GP.?
(i) Salary of Sharmila, when her salary is ₹5,00,000 for the first year and expected to receive yearly increase of 10% .
(ii) Number of bricks needed to make each step, if the staircase has total 30 steps. Bottom step needs 100 bricks and each successive step needs 2 brick less than the previous step.
(iii) Perimeter of the each triangle, when the mid points of sides of an equilateral triangle whose side is 24 cm are joined to form another triangle, whose mid points in turn are joined to form still another triangle and the process continues indefinitely.

Answer 1

1st is G. P.
2ND IS NOT A G. P.
3RD IS A G. P

Answer 2

i ) Salary received by Sharmila in 1st ,

2nd , 3rd year respectively are

Rs 500000 , Rs 550000 , Rs 605000,..

Here ,

a2/a1 = 550000/500000 = 55/50 = 11/10

a3/a2 = 605000/550000 =605/550 = 11/10

Therefore ,

a2/a1 = a3/a2

So , it is in G.P

______________________________

ii ) Number of bricks that needed to

construct bottom step = 100

Each successive step need 2 brick

less than the previous step ,

then ,

Number of bricks needed to 2nd , 3rd

steps 98 , 96 , ..

Now we can write the list as 100 , 98 , 96,..

Here

a2/a1 = 98/100 = 49/50

a3/a2 = 96/98 = 48/49

a2/a1 ≠ a3/a2

Therefore ,

It is not G.P

____________________________

iii ) From the figure ,

Perimeter of a equilateral triangle

whose side is 24 cm = 3 × 24 = 72 cm

Length of the each side , that can

form mid points of an equilateral

triangle = 12 cm

then ,

perimeter = 3 × 12 = 36 cm

Similarly ,

perimeter of next equilateral triangle

= 3 × 6 = 18 cm

Now ,

we can write the list 72 , 36 , 18 , ....

a2/a1 = 36/72 = 1/2

a3/a2 = 18/36 = 1/2

Therefore ,

a2/a1 = a3/a2

It form a G.P

*****