## EXERCISE 9.1

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#### Question 1:

Write the first five terms of the sequences whose n^{th} term is

#### Answer:

Substituting *n* = 1, 2, 3, 4, and 5, we obtain

Therefore, the required terms are 3, 8, 15, 24, and 35.

#### Question 2:

Write the first five terms of the sequences whose n^{th} term is

#### Answer:

Substituting *n* = 1, 2, 3, 4, 5, we obtain

Therefore, the required terms are.

#### Question 3:

Write the first five terms of the sequences whose n^{th} term is *a*_{n} = 2^{n}

#### Answer:

*a*_{n} = 2^{n}

Substituting* n* = 1, 2, 3, 4, 5, we obtain

Therefore, the required terms are 2, 4, 8, 16, and 32.

#### Question 4:

Write the first five terms of the sequences whose *n*^{th} term is

#### Answer:

Substituting *n *= 1, 2, 3, 4, 5, we obtain

Therefore, the required terms are.

#### Question 5:

Write the first five terms of the sequences whose *n*^{th} term is

#### Answer:

Substituting *n *= 1, 2, 3, 4, 5, we obtain

Therefore, the required terms are 25, –125, 625, –3125, and 15625.

#### Question 6:

Write the first five terms of the sequences whose *n*^{th} term is

#### Answer:

Substituting *n* = 1, 2, 3, 4, 5, we obtain

Therefore, the required terms are

#### Question 7:

Find the 17^{th} term in the following sequence whose *n*^{th} term is

#### Answer:

Substituting *n* = 17, we obtain

Substituting *n* = 24, we obtain

#### Question 8:

Find the 7^{th} term in the following sequence whose *n*^{th} term is

#### Answer:

Substituting *n* = 7, we obtain

#### Question 8:

Find the indicated terms in each of the sequences in Exercises 7 to 10 whose *n*^{th} terms are :

an = n22n ; a7

#### Answer:

Here,

an=n22n.

Substituting *n* = 7, we obtain

#### Question 9:

Find the 9^{th} term in the following sequence whose *n*^{th} term is

#### Answer:

Substituting *n* = 9, we obtain

#### Question 10:

Find the 20^{th} term in the following sequence whose *n*^{th} term is

#### Answer:

Substituting *n *= 20, we obtain

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#### Question 11:

Write the first five terms of the following sequence and obtain the corresponding series:

#### Answer:

Hence, the first five terms of the sequence are 3, 11, 35, 107, and 323.

The corresponding series is 3 + 11 + 35 + 107 + 323 + …

#### Question 12:

Write the first five terms of the following sequence and obtain the corresponding series:

#### Answer:

Hence, the first five terms of the sequence are

The corresponding series is

#### Question 13:

Write the first five terms of the following sequence and obtain the corresponding series:

#### Answer:

Hence, the first five terms of the sequence are 2, 2, 1, 0, and –1.

The corresponding series is 2 + 2 + 1 + 0 + (–1) + …

#### Question 14:

The Fibonacci sequence is defined by

Find** **

#### Answer: