Question

The 5 nd 15 term of a ap are 13 nd -17 resp. Find the sum of 1st 21 terms of ap

Answer 1

a5 = 13
a+ (5-1) d = 13
a + 4d =13 [equation 1]

a15 = -17
a+ (15-1)d = -17
a+14d=-17[equation 2]

solve equations 1 and 2
a+4d   =13
a+14d=-17
(-)(-)     (+)
    -10d = 30
          d= 30/-10 = -3 
 a + 4d =13
a+4 x -3 =13
a=13+12
  =25

sn = ?
n=21
a=25
d=-3
sn=n/2 (2a + [n-1] d)
    =21/2 (2 x25 + [21-1] -3 )
    =21/2 (50 + -60 )
    =21/2 x -10
    =21 x -5
    =-105