Question 1: If the term
of a sequence is given by
, write down the first five terms.
Answer:
Given sequence is
Let the first five terms be
Therefore the first five terms are and
Question 2: A sequence is defined by . Show that the first three terms of the sequence are zero and all other terms are positive.
Answer:
The given sequence is
Let the first five terms be
Therefore the first three terms are
And
Therefore will be positive for
Question 3: Find the first four terms of the sequence defined by and
for all.
Answer:
Given and
Question 4: Write the first five terms in each of the following sequences:
i)
ii)
iii)
Answer:
i)
Therefore the first five terms of the given sequence are and
.
ii)
Therefore the first five terms of the given sequence are and
.
iii)
Therefore the first five terms of the given sequence are and
.
Question 5: The Fibonacci sequence is defined by for
. Find
for
.
Answer:
Given:
Therefore for
For
For
For
For
For
Question 6: Show that each of the following sequences is in A.P. Also find the common difference and write 3 more terms in each case.
i)
ii)
iii)
iv)
Answer:
i) Given sequence:
Therefore the common difference
ii) Given sequence:
Therefore the common difference
iii) Given sequence:
Therefore the common difference
iv) Given sequence:
Therefore the common difference
Question 7: The terms of a sequence is given by
. Show that it is an A.P. Also, find its
terms.
Answer:
Given sequence
Therefore the common difference . Therefore the given sequence is an A.P.
Question 8: The terms of a sequence is given by
. Show that it is not an A.P.
Answer:
Given sequence
Therefore
Hence the sequence is not an A.P.