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14.   The Fibonacci sequence is defined by $1 = a _ 1 = a _2 \: \:and \: \: a _n = a _{n-1} + a _{n-2} , n > 2$

Find$\frac{a _{n+1}}{a_n}$, for n = 1, 2, 3, 4, 5

Given : The Fibonacci sequence is defined by

13.  Write the first five terms of each of the sequences in Exercises 11 to 13 and obtain the corresponding series: $a_1 = a_2 = 2, a_n = a_{n - 1}-1, n > 2$

Given :  Hence, five terms of series are  Series

12.  Write the first five terms of each of the sequences in Exercises 11 to 13 and obtain the corresponding series:

$a _ 1 = -1 , a _ n = \frac{a_{n-1}}{n} , n \geq 2$

Given :  Hence, five terms of series are  Series

11.   Write the first five terms of each of the sequences in Exercises 11 to 13 and obtain the corresponding series:

$a_1 = 3, a_n = 3a_{n - 1} + 2\: \: for \: \: all \: \: n > 1$

Given :  Hence, five terms of series are  Series

10.   Find the indicated terms in each of the sequences in Exercises 7 to 10 whose nth terms are:

$a _n = \frac{n ( n-2)}{ n+3 }; a _{20}$

Given :  Put n=20, Hence, value of

9.   Find the indicated terms in each of the sequences in Exercises 7 to 10 whose nth terms are:

$a _ n = ( -1) ^{n-1} n ^ 3 , a _9$

Given :  Put n =9, The value of

8.  Find the indicated terms in each of the sequences in Exercises 7 to 10 whose nth terms are:

$a _n = \frac{n^2 }{2^n } ; a_7$

Given :    Put n=7, Heence, we have

7.  Find the indicated terms in each of the sequences in Exercises 7 to 10 whose nth terms are:

$a _ n = 4 n - 3 ; a _{17} , a _{24}$

Put    Put  n=24, Hence, we have

6.   Write the first five terms of each of the sequences in Exercises 1 to 6 whose nth terms are:

$a _n = n \frac{n^2 + 5}{4}$

Given :  Therefore, the required number of terms

5. Write the first five terms of each of the sequences in Exercises 1 to 6 whose nth terms are:

$a _ n = ( -1) ^{n-1} 5 ^{n+1}$

Given :  Therefore, the required number of terms

4.  Write the first five terms of each of the sequences in Exercises 1 to 6 whose nth terms are:

$a _n = \frac{2n-3 }{6}$

Given :  Therefore, the required number of terms

3.   Write the first five terms of each of the sequences in Exercises 1 to 6 whose nthterms are:

$a _ n = 2 ^n$

Given :  Therefore, required number of terms

2.   Write the first five terms of each of the sequences in Exercises 1 to 6 whose nthterms are:

$a _n = \frac{n }{n+1}$

Given :  Therefore, the required number of terms

1.   Write the first five terms of each of the sequences in Exercises 1 to 6 whose nth terms are:

$a _n = n ( n +2)$

Given :  Therefore, the required number of terms =3, 8, 15, 24, 35
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