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.