# 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.