find the sum of 35 term of an AP whose "P"th term is (p/7) + 12

Question

find the sum of 35 term of an AP  whose "P"th term is (p/7) + 12

anonymous · Answer

is the answer 425??
if it is correct i will elaborate

anonymous · Answer

no

mathmagician · Answer

S=35*12+1/7(1+2+3+...+35)=420+1/7*(1+35+2+34+...+(17+19)+18)=320+1/7*(36*17+18)=320+90=410

anonymous · Answer

no

anonymous · Answer

answer is 510

anonymous · Answer

(p+84)/7
now apply the summation rule to the above with upper limit 35 and lower limit 1
$$((\sum_{1}^{35}p + \sum_{1}^{35}84))/7$$
=(35*18  +  84*35)/7
=510

mathmagician · Answer

oh, really- 12*35=420, not 320, mind calculation error :D so the answer is 510

anonymous · Answer

did you get my method???@srinidhija

anonymous · Answer

yeah , corrct
 sinc pth term is (p/7) +12  => 1st term = 1/7 + 12= 85/7
                                                   2nd trm= 86/7
                                     ==> common difference= 1/7
 
=> sum of 35 term = 35/2 (2x85/7 + (35-1)1/7) 
                                =5 (85 +17)
                               =510

anonymous · Answer

if you use the principle of summation you sum becomes shorter and you can solve them faster!!!! nevermind absorb the method which suits you the most