EXERCISE 19.1
QUESTION 1
If the term
of a sequence is given by
write down its first five terms.
Sol :
Given :
For
= 1
For
= 2
For
= 3
For
= 13
For
= 21
Thus, the first five terms of the sequence are
QUESTION 2
A sequence is defined by Show that the first three terms of
the sequence are zero and all other terms are positive.
Sol :
Given :
For
For
For
For
For
and so on
Thus, the first three terms are zero and the rest of the terms are positive in the sequence .
QUESTION 3
Let be a sequence defined by
and,
for all
.Find the first four terms of the sequence.
Sol :
Given :
And,
for all
Thus, the first four terms of the sequence are
QUESTION 4
Let be a sequence. Write the first five terms in each of the following:
(i)
Sol :
Hence, the five terms are and
(ii)
Sol :
Hence, the five terms are and 5
(iii)
Sol :
Hence, the five terms are and
QUESTION 5
The Fibonacci sequence is defined by for
. Find
for
Sol :
for
Then, we have:
For
For
For
For
For
QUESTION 6
Show that each of the following sequences is an A.P. Also find the common difference
and write 3 more terms in each case.
(i)
Sol :
Thus, the sequence is an A.P. with the common difference being
The next three terms are as follows:
(ii)
Sol :
we have
Thus, the sequence is an A.P. with the common difference being The next three terms are as follows:
(iii)
Sol :
Thus, the sequence is an A.P. with the common difference being The next three terms are as follows:
(iv)
Sol :
Thus, the sequence is an A.P. with the common difference being The next three terms are as follows:
QUESTION 7
The term of a sequence is given by
Show that it is an A.P. Also, find its
7th term.
Sol :
and so on
So, common difference
Thus, the above sequence is an A . P . with the common difference as 2
QUESTION 8
The term of a sequence is given by
Show that it is not an A.P.
Sol :
We have :
= 4
= 11
= 22
= 7
and
= 11
Since,
Hence, it is not an AP.