JEE Main20257 Apr 2025Evening ShiftMathematicsSequences and SeriesActual

Let a _ n be the n ^ th term of an A. P. If S_n=a₁+a₂+a₃+ +a_n=700, a₆=7 and S₇=7 , then a _ n is equal to :

Options

Correct answer

C. 64

Step-by-step solution

S _ n =700= n 2 [2 a +( n -1) d ] ...(i) a₆=7 a+5 d=7 ...(ii) S ₇=7 7 2 (2 a +6 ~d )=7 a+3 d=1 ...(iii) Solve (ii) and (iii) aligned & n 2 (-16+3 n-3)=700 3 n^2-19 n-1400=0 & (3 n+56)( n -25)=0 & a ₂₅= a +24 ~d =-8+24 3 & =-8+72 aligned =64

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