Question

find the numbet terms of A.P.54,51,48.....so the that their sum is 513 soln

Answer 1

here
a=54,
d=-3,

Sn=513,
n=?,

Sn =n/2[2a+(n-1)d],

513=n/2[2×54+(n-1)×(-3)],

513=n/2[108-3(n-1)],

513=n/2[108-3n+3],

1026=n[111-3n],

1026=111n-3n²,

then

3n²-111n+1026=0,

then

n²-37n+342=0,

n²-(19+18)n+342=0,

n²-19n-18n+342=0,

n(n-19)-18(n-19)=0,

(n-19)(n-18)=0,

if
n-19=0,

then
n=19,

if
n-18=0,

then
n=18