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