a1,a2,a3,......a40 are in AP. If a1+a5+a15+a26+a36+a40=105 then sum of the AP is 
A.700                                      B.1400
C.630                                      D.1200

Asked by subhajit.690 | 27th Dec, 2016, 12:14: AM

Expert Answer:

begin mathsize 16px style a 1 plus a 5 plus a 15 plus a 26 plus a 36 plus a 40 equals 105 space space space space space left parenthesis g i v e n right parenthesis
rightwards double arrow a plus left parenthesis a plus 4 d right parenthesis plus left parenthesis a plus 14 d right parenthesis plus left parenthesis a plus 25 d right parenthesis plus left parenthesis a plus 35 d right parenthesis plus left parenthesis a plus 39 d right parenthesis equals 105
rightwards double arrow 6 a plus 117 d equals 105
rightwards double arrow 2 a plus 39 d equals 35 space space space space space space space space..... left parenthesis 1 right parenthesis
N o w comma space S subscript n equals n over 2 left parenthesis a plus l right parenthesis
S subscript 40 equals 40 over 2 left parenthesis a subscript 1 plus a subscript 40 right parenthesis
rightwards double arrow S subscript 40 equals 20 left square bracket a plus left parenthesis a plus 39 d right parenthesis right square bracket
rightwards double arrow S subscript 40 equals 20 left square bracket 2 a plus 39 d right square bracket
rightwards double arrow S subscript 40 equals 20 cross times 35 space space space space space space..... left square bracket F r o m space left parenthesis 1 right parenthesis right square bracket
rightwards double arrow S subscript 40 equals 700
C o r r e c t space o p t i o n space left parenthesis A right parenthesis end style

Answered by Rashmi Khot | 27th Dec, 2016, 09:19: AM