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(nāˆ’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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