Question 1: Show that each one of the following progressions is a G.P.. Also, find the common ratio in each case:

Answer:

Answer:

is a G.P

Question 3: Find:

Answer:

We know,

We know,

We know,

We know,

We know,

We know,

Answer:

Now, when we reverse the G.P., we have

We know,

Question 5: Which term of the progression

Answer:

is

term

Question 6: Which term of the G.P.:

Answer:

?

term

term

term

term

Question 7: Which term of the progression ?

Answer:

term

Answer:

Answer:

… … … … … i)

… … … … … ii)

Dividing ii) by i) we get

Substituting in i) we get

Question 10:The term of the G.P. is times the term and term is . Find the G.P.

Answer:

Question 11: If the G.P.’s have their terms equal, find the value of .

Answer:

… … … … … i)

… … … … … ii)

From i) and ii) we get

Question 12: The term of a G.P. are respectively, prove tht .

Answer:

… … … … … i)

… … … … … ii)

… … … … … iii)

. Hence proved.

Question 13: The term of a G.P. is square of its term and the first term is . Find its term.

Answer:

Question 14: In a G.P. the term is and the term is . Find the term.

Answer:

… … … … … i)

… … … … … ii)

Dividing ii) and i) we get

Substituting in i) we get

Question 15: If are different real numbers such that

, then show that are in G.P.

Answer:

Since all the terms are square, therefore they cannot be less than zero. Hence,

are in G.P.

Answer:

Take the first two terms

Apply componendo and dividendo we get

… … … … … i)

Similarly, Take the last two terms

Apply componendo and dividendo we get

… … … … … ii)

are in G.P.

Question 17: If the and the terms of a G.P. are respectively, show that term is

Answer:

… … … … … i)

… … … … … ii)

Dividing i) by ii)

… … … … … i)

Substituting the value of r in ii) we get

… … … … … ii)

… … … … … iii)

Substituting i) and ii) in iii) we get