Question

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

Answer 1

`\boxed{\sf a_n=(a_(n-1))/(10)* 4,n\gt 1}`

Lets verify

`\\ \sf\longmapsto a_2=(a_1)/(10)* 4`

`\\ \sf\longmapsto a_2=(500)/(10)* 4=50(4)=200`

And

`\\ \sf\longmapsto a_3=(a_2)/(10)* 4`

`\\ \sf\longmapsto a_3=(200)/(10)* 4=20(4)=80`

And

`\\ \sf\longmapsto a_4=(a_3)/(10)* 4`

`\\ \sf\longmapsto a_4=(80)/(10)* 4=8(4)=32`

Hence verified

Lets predict next term

`\\ \sf\longmapsto a_5=(a_4)/(10)* 4`

`\\ \sf\longmapsto a_5=(32)/(10)* 4=3.2* 4=12.8`