Sasi Math (Revised for 1024)

Scroll:Sequences and series >> Worked Examples >> saq (4213)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.

Write the each of the following sequences. (use /)

a₁ = -s1 ,

a₄=	a₄-1	n >4 and Å n£N
	4+2

Answer:_______________

Write the each of the following sequences. (use /)

a₁ = $\frac{-1}{4}$ ,

an=	a $\frac{-1}{4}$	n >2 and Å n£N
	n+2

Answer:_______________

Write the sequence whose n^th term is given by n=3

Cn	n(n+1)(2n+1)	n £ N
	6

Answer:_______________

Write the first five terms of each of the following sequences.

Given that terms K₁ = K₂ = 1 and K_n-1 + K_n-2, n = 3,4,5....

Answer:_______________

Write the each of the following sequences. (use /)

a₁ = -s1 ,

a₅=	a₅-1	n >5 and Å n£N
	5+2

Answer:_______________

Write the each of the following sequences. (use /)

a₁ = $\frac{-1}{4}$ ,

an=	a $\frac{-1}{4}$	n >2 and Å n£N
	n+2

Answer:_______________

Write the sequence whose n^th term is given by n=1

Cn	n(n+1)(2n+1)	n £ N
	6

Answer:_______________

Write the first five terms of each of the following sequences.

Given that terms Y₁ = Y₂ = 5 and Y_n-1 + Y_n-2, n = 3,4,5....

Answer:_______________

Write the each of the following sequences. (use /)

a₁ = -s1 ,

a₁=	a₁-1	n >1 and Å n£N
	1+2

Answer:_______________

10)

Write the each of the following sequences. (use /)

a₁ = $\frac{-1}{4}$ ,

an=	a $\frac{-1}{4}$	n >2 and Å n£N
	n+2

Answer:_______________

Write the each of the following sequences. (use /)

a₁ = -s1 ,

a₄=	a₄-1	n >4 and Å n£N
	4+2

Answer: $\frac{-1}{6}$

SOLUTION 1 :

Given

a₁ = -1 ,

a_n=	a_n_-1	n > 1
	n+2

a₄=	a₁	$\frac{-1}{6}$
	4+2

Write the each of the following sequences. (use /)

a₁ = $\frac{-1}{4}$ ,

an=	a $\frac{-1}{4}$	n >2 and Å n£N
	n+2

Answer: 80

SOLUTION 1 :

Given

a₁ = -1 ,

a_n=	a_n_-1	n > 1
	n+2

a₂=	$\frac{-1}{4}$	$\frac{-1}{20}$
	3+2

Write the sequence whose n^th term is given by n=3

Cn	n(n+1)(2n+1)	n £ N
	6

Answer: 14

SOLUTION 1 :

Here,

Here Cn	n(n+1)(2 n+1)	n £ N
	6

n = 3,Cn	3(3+1) x (2x3)+1)	=	(3)x(4)x(7)
	6		6

n = 3	84	=	14
	6

Write the first five terms of each of the following sequences.

Given that terms L₁ = L₂ = 1 and L_n-1 + L_n-2, n = 3,4,5....

Answer: 1,1,2,3,5

SOLUTION 1 :

Now , L₁ = 1, L₂ = 1

L₃ = L₂+ L₁ = 1 + 1 = 2

L₄ = L₃ + L₂ = 2 + 1 = 3

L₅ = L₄ + L₃ = 3 + 2 = 5

Write the each of the following sequences. (use /)

a₁ = -s1 ,

a₅=	a₅-1	n >5 and Å n£N
	5+2

Answer: $\frac{-1}{7}$

SOLUTION 1 :

Given

a₁ = -1 ,

a_n=	a_n_-1	n > 1
	n+2

a₅=	a₁	$\frac{-1}{7}$
	5+2

Write the each of the following sequences. (use /)

a₁ = $\frac{-1}{4}$ ,

an=	a $\frac{-1}{4}$	n >2 and Å n£N
	n+2

Answer: 80

SOLUTION 1 :

Given

a₁ = -1 ,

a_n=	a_n_-1	n > 1
	n+2

a₂=	$\frac{-1}{4}$	$\frac{-1}{20}$
	3+2

Write the sequence whose n^th term is given by n=1

Cn	n(n+1)(2n+1)	n £ N
	6

Answer: 1

SOLUTION 1 :

Here,

Here Cn	n(n+1)(2 n+1)	n £ N
	6

n = 1,Cn	1(1+1) x (2x1)+1)	=	(1)x(2)x(3)
	6		6

n = 1	6	=	1
	6

Write the first five terms of each of the following sequences.

Given that terms A₁ = A₂ = 5 and A_n-1 + A_n-2, n = 3,4,5....

Answer: 5,5,10,15,25

SOLUTION 1 :

Now , A₁ = 5, A₂ = 5

A₃ = A₂+ A₁ = 5 + 5 = 10

A₄ = A₃ + A₂ = 10 + 5 = 15

A₅ = A₄ + A₃ = 15 + 10 = 25

Write the each of the following sequences. (use /)

a₁ = -s1 ,

a₁=	a₁-1	n >1 and Å n£N
	1+2

Answer: $\frac{-1}{3}$

SOLUTION 1 :

Given

a₁ = -1 ,

a_n=	a_n_-1	n > 1
	n+2

a₁=	a₁	$\frac{-1}{3}$
	1+2

10)

Write the each of the following sequences. (use /)

a₁ = $\frac{-1}{4}$ ,

an=	a $\frac{-1}{4}$	n >2 and Å n£N
	n+2

Answer: 80

SOLUTION 1 :

Given

a₁ = -1 ,

a_n=	a_n_-1	n > 1
	n+2

a₂=	$\frac{-1}{4}$	$\frac{-1}{20}$
	3+2