how many terms of an AP 5,8,11,..... add upto 670

Here a=5 , d=3

Sn = 670

--> n/2[ 2a + (n-1)d] = 670

-->n/2 [ 10 + (n-1)3] = 670

-->n/2 [ 10 + 3n-3] =670

--> n/2[7+3n]=670

-->n[7+3n] = 1340

-->3n2 + 7n = 1340

--> 3n2 + 7n - 1340 = 0

-->3n2 + 67n - 60n -1340 = 0

--> n(3n + 67) -20(3n +67)= 0 

-->(n-20)(3n + 67) = 0

--> n=20  or n= -67/3

-->n=20  {since -67/3 is not admissible]

--> 20 terms of the A.P add upto 670.

Hope it helps... Cheers..