The sequence $u_1,u_2,u_3...$ can be abbreviated as $(u_n)$.

You are given that

• $(u_n)$ is an arithmetic progression with first term $a$ and common difference $b$
• $(v_n)$ is an arithmetic progression with first term $c$ and common difference $d$
• $(u_n + v_n)$ is an arithmetic progression with first term 5 and common difference 8 (the terms are $u_1 + v_1, u_2 + v_2, u_3 + v_3, ...$)
• $(u_nv_n)$ is the sequence $(w_n+k(n−1)^2)$ where $(w_n)$ is an arithmetic progression with first term 6 and common difference 7, and where $k$ is a constant (the terms are $u_1v_1, u_2v_2, u_3v_3, ...$)

Find $| a \times b \times c \times d|$

Source: Ritangle, 2021

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