Question

Complete the recursive formula of the geometric sequence 500,200,80,32,​

Answer 1

$\boxed{\sf a_n=\dfrac{a_{n-1}}{10}\times 4,n\gt 1}$

Lets verify

$\\ \sf\longmapsto a_2=\dfrac{a_1}{10}\times 4$

$\\ \sf\longmapsto a_2=\dfrac{500}{10}\times 4=50(4)=200$

And

$\\ \sf\longmapsto a_3=\dfrac{a_2}{10}\times 4$

$\\ \sf\longmapsto a_3=\dfrac{200}{10}\times 4=20(4)=80$

And

$\\ \sf\longmapsto a_4=\dfrac{a_3}{10}\times 4$

$\\ \sf\longmapsto a_4=\dfrac{80}{10}\times 4=8(4)=32$

Hence verified

Lets predict next term

$\\ \sf\longmapsto a_5=\dfrac{a_4}{10}\times 4$

$\\ \sf\longmapsto a_5=\dfrac{32}{10}\times 4=3.2\times 4=12.8$