Question

the sum of first 11 tems of an a.p is 19 and the sum of first 19 terms of an a.p is 11 find the sum of first 30 terms

Answer 1

S11=19 .......................(given)
11/2[2a+(11-1)d=19.........formula sn
11/2[2a+10d]=19
11/2×2(a+5d)=19
11(a+5d)=19
11a+55d=19..............................(1)
S19=11.......................(given)
19/2[2a+(19-1)d]=11.......formula sn
19/2[2a+18d]=11
19/2×2(a+9d)=11
19(a+9d)=11
19a+171d=11....................(2)
multiply eq(1) by 19&eq(2) by 11
209a+1045d=361.......(3)
209a+1981d=121..........(4)
subtracting eq(4) from(3)
-936d=240
d=-936/240
d=-3.9
substitute d=-3.9 in eq(1)
a=21.22
S30=30/2[2(21.22)+(30-1)-3.9]
WE GET
S30=-1059.9(aproximately)
lets hope this helps