Question Number 10347 by konen last updated on 04/Feb/17

A=1+2+3+...+n−2  B=15+16+.....+n  A−B=42⇒n=?

Answered by mrW1 last updated on 05/Feb/17

A=Σ_(k=1) ^(n−2) k=(((n−2)(n−1))/2)=((n^2 −3n+2)/2)  B=Σ_(k=15) ^n k=(((n+15)(n−14))/2)=((n^2 +n−210)/2)  A−B=42  ((n^2 −3n+2−n^2 −n+210)/2)=42  ((212−4n)/2)=42  n=((212−84)/4)=32

Answered by arge last updated on 05/Feb/17

      n=((2S_n )/(a_1 +a_n ))    n=((a_n −a_1 )/d) +1    ((2S_n )/(a_1 +a_n )) =((a_n −a_1 )/d)  +1  d=1  S_n =(((a_1 +a_n )(a_n −a_1 +d))/(2d))    S_n A=(((n−2)(n−1))/2)  d=1    S_n B=(((n−14)(n+15))/2)    S_n A−S_n B=42    (((n−2)(n−1))/2) − (((n−14)(n+15))/2) =42    n= 32∵∵∵Rta