A) \[{{n}^{3}}+{{n}^{2}}+1\]
B) \[{{n}^{3}}-{{n}^{2}}+1\]
C) \[{{n}^{3}}-{{n}^{2}}\]
D) \[{{n}^{3}}+{{n}^{2}}\]
Correct Answer: B
Solution :
Given, \[{{a}_{0}}=1,\,\,{{a}_{n+1}}=3{{n}^{2}}+n+{{a}_{n}}\] \[\Rightarrow \] \[{{a}_{1}}=3(0)+0+{{0}_{0}}=1\] and \[{{a}_{2}}=3{{(1)}^{2}}+1+{{a}_{1}}=3+1+1=5\] From option (b), Let \[P(n)={{n}^{3}}-{{n}^{2}}+1\] \[\therefore \] \[P(0)=0-0+1=1={{a}_{0}}\] \[P(1)={{1}^{3}}-{{1}^{2}}+1=1={{a}_{1}}\] and \[P(2)={{(2)}^{3}}-{{(2)}^{2}}+1=5={{a}_{2}}\] Hence, option (b) is correct.You need to login to perform this action.
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