Question

find how many term of the AP.54,51,48...must be taken so that their sum is 513 .Explain the double answer

Answer 1

54,51,48,... Ap
first term = a=54, common difference = d=a2-a1=51-54=-3

sum of n terms =513
n/2[2a+(n-1)d] =513
n/2([2*54+(n-1)(-3)]=513
n/2[108-3n+3] =513
(n/2)*3[36-n+1]=513

n[37-n]= 513*2/3
37n-n²=171*2
n²-37n+342=0
n²-18n-19n+18*19=0
n(n-18)-19(n-18)=0
(n-18)(n-19)=0
n-18=0 or n-19=0
therefore
n= 18 or n=19
sum of 18 terms or sum of 19 terms of the given AP is equal to 513