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Write the correct number in the given boxes from the following A.P.: (i) 1, 8, 15, 22, . . . (ii) 3, 6, 9, 12, . . . (iii) -3, -8, -13, -18, . . . (iv) 70, 60, 50, 40, . . .

Write the correct number in the given boxes from the following A. P.

(i) 1, 8, 15, 22, ... Here \(a = \square, t_1 = \square, t_2 = \square, t_3 = \square\); \(t_2 - t_1 = \square - \square = \square\); \(t_3 - t_2 = \square - \square = \square\) ∴ \(d = \square\)

(ii) 3, 6, 9, 12, ... Here \(t_1 = \square, t_2 = \square, t_3 = \square, t_4 = \square\); \(t_2 - t_1 = \square\), \(t_3 - t_2 = \square\) ∴ \(d = \square\)

(iii) −3, −8, −13, −18, ... Here \(t_3 = \square, t_2 = \square, t_4 = \square, t_1 = \square\); \(t_2 - t_1 = \square\), \(t_3 - t_2 = \square\) ∴ \(a = \square\), \(d = \square\)

(iv) 70, 60, 50, 40, ... Here \(t_1 = \square, t_2 = \square, t_3 = \square\), ... ∴ \(a = \square\), \(d = \square\)

1 answer

Answer: (i) d = 7 (ii) d = 3 (iii) a = −3, d = −5 (iv) a = 70, d = −10

(i) \(a = 1\), \(t_1 = 1\), \(t_2 = 8\), \(t_3 = 15\); \(t_2 - t_1 = 8 - 1 = 7\); \(t_3 - t_2 = 15 - 8 = 7\); ∴ \(d = 7\).

(ii) \(t_1 = 3\), \(t_2 = 6\), \(t_3 = 9\), \(t_4 = 12\); \(t_2 - t_1 = 3\), \(t_3 - t_2 = 3\); ∴ \(d = 3\).

(iii) \(t_3 = -13\), \(t_2 = -8\), \(t_4 = -18\), \(t_1 = -3\); \(t_2 - t_1 = -8 - (-3) = -5\), \(t_3 - t_2 = -13 - (-8) = -5\); ∴ \(a = -3\), \(d = -5\).

(iv) \(t_1 = 70\), \(t_2 = 60\), \(t_3 = 50\); ∴ \(a = 70\), \(d = 60 - 70 = -10\).

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report
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