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Question Number 74141 by MASANJAJ last updated on 19/Nov/19

Commented by TawaTawa last updated on 19/Nov/19

d) a = 5 Forth term = ar^3 = 40 ∴ 5r^3 = 40 ∴ r^3 = ((40)/5) ∴ r^3 = 8 ∴ r^3 = 2^3 ∴ r = 2 ∴ x = second term = ar = 5 × 2 = 10 ∴ y = third term = ar^2 = 5 × 2^2 = 5 × 4 = 20

$$\left.\mathrm{d}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{a}\:\:=\:\:\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{Forth}\:\mathrm{term}\:\:=\:\:\:\mathrm{ar}^{\mathrm{3}} \:\:=\:\:\mathrm{40} \\ $$$$\:\:\:\:\:\:\:\therefore\:\:\:\:\:\:\:\mathrm{5r}^{\mathrm{3}} \:\:=\:\:\mathrm{40} \\ $$$$\:\:\:\:\:\:\:\therefore\:\:\:\:\:\:\:\mathrm{r}^{\mathrm{3}} \:\:=\:\:\frac{\mathrm{40}}{\mathrm{5}} \\ $$$$\:\:\:\:\:\:\:\therefore\:\:\:\:\:\:\:\mathrm{r}^{\mathrm{3}} \:\:=\:\:\mathrm{8} \\ $$$$\:\:\:\:\:\:\:\therefore\:\:\:\:\:\:\:\mathrm{r}^{\mathrm{3}} \:\:=\:\:\mathrm{2}^{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\therefore\:\:\:\:\:\:\:\mathrm{r}\:\:=\:\:\mathrm{2} \\ $$$$\therefore\:\:\:\:\:\:\:\mathrm{x}\:\:\:=\:\:\:\mathrm{second}\:\mathrm{term}\:\:=\:\mathrm{ar}\:\:\:=\:\:\:\mathrm{5}\:×\:\mathrm{2}\:\:=\:\:\mathrm{10} \\ $$$$\therefore\:\:\:\:\:\:\:\mathrm{y}\:\:\:=\:\:\:\mathrm{third}\:\mathrm{term}\:\:=\:\mathrm{ar}^{\mathrm{2}} \:\:\:=\:\:\:\mathrm{5}\:×\:\mathrm{2}^{\mathrm{2}} \:\:=\:\:\mathrm{5}\:×\:\mathrm{4}\:\:=\:\:\mathrm{20} \\ $$

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