Question

nth term of 1^2+3^2+5^2+7^2......n terms is​

Answer 1

Answer:

Step-by-step explanation:

To find the n  

th

 term we have to look the succesive difference of the sequence

8,−16,0,−64,−200,−432.....

8,−16,−64,−136,−232.....

−24,−48,−72,−96....

−24,−24,−24

Let u  

n

​  

=A+Bn+Cn  

2

+Dn  

3

 

u  

1

​  

=8

⇒A+B+C+D=8.....(i)

u  

2

​  

=−16

⇒A+2B+4C+8D=−16.....(ii)

u  

3

​  

=0

⇒A+3B+9C+27D=0.....(iii)

u  

4

​  

=−64

⇒A+4B+16C+64D=−64....(iv)

Solving (i),(ii),(iii) and (iv)

⇒A=0,B=0,C=12,D=−4

⇒u  

n

​  

=12n  

2

−4n  

3

 

S  

n

​  

=∑u  

n

​  

 

⇒S  

n

​  

=12∑n  

2

−4∑n  

3

 

⇒S  

n

​  

=12−4[  

4

n  

2

(n+1)  

2

 

​  

]

⇒S  

n

​  

=−n(n+1)(n  

2

−3n−2)

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