Let A_r, r=1,2, .29 be arithmetic means between 303 and -57 where A_rA_ r+1 =1,2, 2 . If S be the sum of these means, then the value of [ S (A₁₄-12 ) |A_r |_ min. ] . |Note: [k] denotes greatest integer less than or equal to k and |A_r |_

Question

Let A_r, r=1,2, .29 be arithmetic means between 303 and -57 where A_r>A_ r+1 =1,2, 2 . If S be the sum of these means, then the value of [ S (A₁₄-12 ) |A_r |_ min. ] . |Note: [k] denotes greatest integer less than or equal to k and |A_r |_ min . denotes the minimum value of |A_r | .]

Quantrex Academy · Accepted Answer

Correct answer: 9

aligned & d= -57-303 30 =-12 & A_r=303+r (-12) 0 r 303 12 25 . & A₂₅=303+25(-2)=3 & |A_r |_ min = |A₂₅ |=3 & S (A₁₄-12 ) |A_r |_ min. = 29 (A₁+A₂₉ ) 2 (A₁₅ ) 3 = 29 3 & [ S (A₁₄-12 ) |A_r |_ ]=9 & aligned

Let A_r, r=1,2, .29 be arithmetic means between 303 and -57 where A_r>A_ r+1 =1,2, 2 . If S be the sum of these means, then the value of [ S (A₁₄-12 ) |A_r |_ min. ] . |Note: [k] denotes greatest integer less than or equal to k and |A_r |_ min . denotes the minimum value of |A_r | .]

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