Here is an $$AP:10,13,...,94,$$ where $$a=10, d=3$$ and $$a_n=l=94$$
So for finding the sum of first 14 terms:
$$Sn = n/2 *[2a+(n-1)d] = 14/2 * [2*10+(14-1)3] = 413$$ $$Sn = n/2 *[a+l] = 14/2 * [10+94] = 728$$
Why am I getting 2 different answers? Where am I wrong? I have checked many times but still can't find my mistake?
You are assuming that 94 is the 14th term but first check whether 94 is really the 14th term
We have $$a_n=a+(n-1)d$$ $$94=10+(n-1)3$$
$$84=(n-1)3$$
$$n=29$$
Thus 94 is not 14th term it is 29th term so you are summing till the 29th term