Kane is training for a marathon. He starts by running 3 miles during every training session. Each week plans to increase the dista

Kane is training for a marathon. He starts by running 3 miles during every training session. Each week plans to increase the distance of his run by 1/4 mile.

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  1. Complete Question :- Kane is training for a marathon. He starts by running 3 miles during every training session each week plans to increase the distance of his runs by 1/4 mile. Let w be the number of weeks. Write and expression to show the distance kane runs in a training session after w weeks ?

    Solution :

    → first week kane runs = a = 3 miles .

    → increased speed every week = d = (1/4) mile .

    → Total week = n = w .

    we know that,

    • Tn = a + (n – 1)d where
    • a = first term .
    • n = total terms .
    • d = common difference .

    so,

    → Tw = a + (w – 1)d

    → Tw = 3 + (w – 1)(1/4)

    → Tw = 3 + (w/4) – (1/4)

    → Tw = (3 * 4 + w – 1)/4

    → Tw = (12 + w – 1) / 4

    → Tw = (11 + w)/4 (Ans.)

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