Mathematics: Given a term in a geometric sequence and the common ratio find the first five terms and the formula representing the nth term. a1 = 4, r = 5

Given a term in a geometric sequence and the common

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sswd

31.05.2020

Mathematics

what was the reall answer? I could use bit of help!

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JvGaming2001

08.04.2021

Mathematics

$\large\boxed{r^{32}}$

Step-by-step explanation:

$\bold{METHOD\ 1:}\\\\\sqrt{r^{64}}=\sqrt{r^{32\cdot2}}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\sqrt{(r^{32})^2}\qquad\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=r^{32}\\\\\bold{METHOD\ 2:}\\\\\text{Use}\ \sqrt{a}=a^{\frac{1}{2}}\\\\\sqrt{r^{64}}=\left(r^{64}\right)^\frac{1}{2}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=r^{64\cdot\frac{1}{2}}=r^{32}$

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Given a term in a geometric sequence and the common ratio find the first five terms and the formula representing the nth term. a1 = 4, r = 5

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