AP EAMCET202421 May 2024Evening ShiftMathematicsFunctionsActual

If 1.3 .5+3.5 .7+5.7 .9+ n terms =n(n+1) f(n)-3 n , then f(1)=

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Correct answer

A. 9

Step-by-step solution

1 3 5+3 5 7+5 7 9+ . n terms aligned & T_n=(2 n-1)(2 n+1)(2 n+3)=8 n^3+12 n^2-2 n-3 & S_n= T_n=8 n^3+12 n^2-2 n-3 1 aligned aligned & = 8(n(n+1))^2 4 + 12 n(n+1)(2 n+1) 6 - 2 n(n+1) 2 -3 n & =2 n^4+8 n^3+7 n^2-2 n=n(n+1) f(n)-3 n aligned aligned & f(x)= n (2 n^3+8 n^2+7 n+1 ) n(n+1) & f(1)= 2+8+7+1 2 =9 aligned

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