# So little information!!!

Algebra Level 5

An arithmetic progression of $$n$$ terms has the following characteristics:

1. The first term $$a$$ is a positive odd integer
2. The common difference $$d$$ is a positive integer
3. The terms of the progression alternate between odd and even integers.

Now, it is given that

$\left(T_2 + T_4 + T_6 + T_8 + \ldots\right) - \left(T_1 + T_3 + T_5 + T_7 + \ldots\right) = 501$

Find the value of $$p$$ if $$n \equiv p \pmod{4}$$

Clarification: $$T_k$$ represents the $$k$$-th term in the progression

Inspiration (Recommended to solve this first)

×