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Mathematical sequence problem in junior high school
(1) geometric progression's fourth item 5,-15,45, ... is (-135).

Its common ratio is -3, so the fourth term =-45 * 3 =- 135.

(2) If a certain column number a 1, a2, a3… is a geometric series, and the common ratio is q, then the above provisions of agricultural tools are a2/a 1=q, a4a3=q… so A2 = A1q; a3 = a2q = a 1 * q * q = a 1q∧2; a4 = a3q = AQ * q = a 1q∧2; ... then = (an = a 1 * q (n- 1)) (expressed by an and q algebra)

(3) The second term of a geometric series is 10, and the third term is 20. Find its 1 and 4 items.

Common ratio =20/ 10=2

So a 1= 10/2=5.

a4=20*2=40