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