Scroll:Sequences and series >> Worked Examples >> saq (4212)

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.


 

1)  

 Write the  sequence whose nth term is given by n=7


Cn
 		 n(n+1)(2n+1)
n £ N
 
6



Answer:_______________




2)  

 Write the  sequence whose nth term is given by n=1


Cn
 		 n(n+1)(2n+1)
n £ N
 
6



Answer:_______________




3)  

 Write the  sequence whose nth term is given by n=9


Cn
 		 n(n+1)(2n+1)
n £ N
 
6



Answer:_______________




4)  

 Write the  sequence whose nth term is given by n=11


Cn
 		 n(n+1)(2n+1)
n £ N
 
6



Answer:_______________




5)  

 Write the  sequence whose nth term is given by n=13


Cn
 		 n(n+1)(2n+1)
n £ N
 
6



Answer:_______________




6)  

 Write the  sequence whose nth term is given by n=4


Cn
 		 n(n+1)(2n+1)
n £ N
 
6



Answer:_______________




7)  

 Write the  sequence whose nth term is given by n=8


Cn
 		 n(n+1)(2n+1)
n £ N
 
6



Answer:_______________




8)  

 Write the  sequence whose nth term is given by n=3


Cn
 		 n(n+1)(2n+1)
n £ N
 
6



Answer:_______________




9)  

 Write the  sequence whose nth term is given by n=2


Cn
 		 n(n+1)(2n+1)
n £ N
 
6



Answer:_______________




10)  

 Write the  sequence whose nth term is given by n=10


Cn
 		 n(n+1)(2n+1)
n £ N
 
6



Answer:_______________




 

1)  

 Write the  sequence whose nth term is given by n=7


Cn
 		 n(n+1)(2n+1)
n £ N
 
6


Answer: 140


SOLUTION 1 :

 Here, 


Here  Cn
 		 n(n+1)(2 n+1)
n £ N
 
6

 


n = 7,Cn
 		 7(7+1) x (2x7)+1)
=
 		 (7)x(8)x(15)
6 6

 

n = 7
 

 840
=
 		140 
6
 

 



2)  

 Write the  sequence whose nth 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
 

 



3)  

 Write the  sequence whose nth term is given by n=9


Cn
 		 n(n+1)(2n+1)
n £ N
 
6


Answer: 285


SOLUTION 1 :

 Here, 


Here  Cn
 		 n(n+1)(2 n+1)
n £ N
 
6

 


n = 9,Cn
 		 9(9+1) x (2x9)+1)
=
 		 (9)x(10)x(19)
6 6

 

n = 9
 

 1710
=
 		285 
6
 

 



4)  

 Write the  sequence whose nth term is given by n=11


Cn
 		 n(n+1)(2n+1)
n £ N
 
6


Answer: 506


SOLUTION 1 :

 Here, 


Here  Cn
 		 n(n+1)(2 n+1)
n £ N
 
6

 


n = 11,Cn
 		 11(11+1) x (2x11)+1)
=
 		 (11)x(12)x(23)
6 6

 

n = 11
 

 3036
=
 		506 
6
 

 



5)  

 Write the  sequence whose nth term is given by n=13


Cn
 		 n(n+1)(2n+1)
n £ N
 
6


Answer: 819


SOLUTION 1 :

 Here, 


Here  Cn
 		 n(n+1)(2 n+1)
n £ N
 
6

 


n = 13,Cn
 		 13(13+1) x (2x13)+1)
=
 		 (13)x(14)x(27)
6 6

 

n = 13
 

 4914
=
 		819 
6
 

 



6)  

 Write the  sequence whose nth term is given by n=4


Cn
 		 n(n+1)(2n+1)
n £ N
 
6


Answer: 30


SOLUTION 1 :

 Here, 


Here  Cn
 		 n(n+1)(2 n+1)
n £ N
 
6

 


n = 4,Cn
 		 4(4+1) x (2x4)+1)
=
 		 (4)x(5)x(9)
6 6

 

n = 4
 

 180
=
 		30 
6
 

 



7)  

 Write the  sequence whose nth term is given by n=8


Cn
 		 n(n+1)(2n+1)
n £ N
 
6


Answer: 204


SOLUTION 1 :

 Here, 


Here  Cn
 		 n(n+1)(2 n+1)
n £ N
 
6

 


n = 8,Cn
 		 8(8+1) x (2x8)+1)
=
 		 (8)x(9)x(17)
6 6

 

n = 8
 

 1224
=
 		204 
6
 

 



8)  

 Write the  sequence whose nth 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
 

 



9)  

 Write the  sequence whose nth term is given by n=2


Cn
 		 n(n+1)(2n+1)
n £ N
 
6


Answer: 5


SOLUTION 1 :

 Here, 


Here  Cn
 		 n(n+1)(2 n+1)
n £ N
 
6

 


n = 2,Cn
 		 2(2+1) x (2x2)+1)
=
 		 (2)x(3)x(5)
6 6

 

n = 2
 

 30
=
 		5 
6
 

 



10)  

 Write the  sequence whose nth term is given by n=10


Cn
 		 n(n+1)(2n+1)
n £ N
 
6


Answer: 385


SOLUTION 1 :

 Here, 


Here  Cn
 		 n(n+1)(2 n+1)
n £ N
 
6

 


n = 10,Cn
 		 10(10+1) x (2x10)+1)
=
 		 (10)x(11)x(21)
6 6

 

n = 10
 

 2310
=
 		385 
6