In a arithmetic progression sum of first four terms sum :
$$a_1+a_2+a_3+a_4=124$$
and sum of last four terms :
$$a_n+a_{n-1}+a_{n-2}+a_{n-3}=156$$
and sum of arithmetic progression is :
$$S_n=350$$
$$n=?$$
How to find $n$? I tried using arithmetic progression sum formulas but getting negative or fractional numbers.
Best Answer
One has $a_1+a_2+a_3+a_4+a_{n-3}+a_{n-2}+a_{n-1}+a_n=280$. The mean of those eight terms is $35$, so the mean of $a_1,\ldots,a_n$ is also $35$. The sum of those $n$ terms is $n$ times their mean, and is $350$. So now you can read off $n$.