Question

considere a p.g(a) de razao q=7√3 e a15= 5 determine a1

Answer 1

$a_{n}=a_1\cdot{q}^{n-1},\quad\forall{n}\in\mathbb{N}^*$


$q=7\sqrt3\qquad\qquad\qquad{a}_{15}=5\qquad\qquad\qquad{a}_1=\,\,?$


$a_{n}=a_1\cdot{q}^{n-1}\\\\a_{15}=a^{1}\cdot{q}^{15-1}\longrightarrow{a}_{15}=a_1\cdot{q}^{14}\\\\5=a_1\cdot\left(7\sqrt{3}\right)^{14}\\\\5=a_1\cdot\left(\sqrt{7^2\cdot3}\right)^{14}\\\\5=a_1\cdot((7^2\cdot3)^{\frac{1}{2}})^{^{14}}\\\\5=a_1\cdot(7^2\cdot3)^{7}\\\\\boxed{\boxed{a_1=\dfrac{5}{(7^2\cdot3)^7}}}\\\\\\\text{Se preferir numericamente:}\\\\a_1=\dfrac{5}{(147)^7}\\\\\boxed{\boxed{a_1=3,3709216711462393411275506670238\cdot10^{-15}}}$