Question

Find the 10th and 20th terms of the GP with first term 3 and common ratio 2.

Answer 1

Step-by-step explanation:

$\:\:\:{n}^{th} \: term \: of \: a \: GP \: is \: given \: as : \\ \:\:\:t_n = a{r}^{n - 1} \: where \: \\ \:\:\:a = first \: term = 3 \\\:\:\: r = common \: ratio = 2 \\ \implies \: t_{10} = 3 \times {2}^{10 - 1} \\ \implies \: t_{10} = 3 \times {2}^{9} \\ \implies \: t_{10} = 3 \times 512 \\ \implies \: \huge \fbox{ t_{10} = 1536} \\ \:\:\:next \\ \:\:\:t_{20} = 3 \times {2}^{20 - 1} \\ \implies \: t_{20} = 3 \times {2}^{19} \\ \implies \: t_{20} = 3 \times 524288 \\ \implies \huge \fbox{ t_{20} =1,572,864 }$

Answer 2

Answer:

Find the 10th and 20th terms of the GP with first term 3 and common ratio 2.