In an arithmetic sequence, the 6th term is half the fourth term and the third term is 15.

i) Find the first term and the common difference

ii) How many terms are needed to give a sum that is less than 65?

I've done part (i) and found a=21 and d=-3, but I'm having trouble with the second part. Here's what I've got so far:

S_{n }= n/2{2a+(n-1)d}

S_{n }= n/2{2(21) + (n-1)(-3)}

S_{n }= n/2{45-3n}

(n/2){45-3n} < 65

n{45-3n} < 130

45n -3n^{2 }< 130

I think I'm on the right track (I think???)...but I don’t think the quadratic inequality isn't giving me whole numbers if I solve for values of n so I’ve gone wrong somewhere. Any help? Thanks