Question

Find a2 of the geometric sequence if a5 is 12 and a8 is 3/2

Answer 1

`a_5=12`

And

`a_8=(3)/(2)`
`a_5=a_1\cdot r^(5-1)=a_1\cdot r^4`
`a_8=a_1\cdot r^7`
`a_5\cdot r^3=a_8`
`12\cdot r^3=(3)/(2)`
`r^3=(3)/(24)`
`r=\sqrt[3]{(3)/(24)}`

So,

`a_2=(a_5)/(r^3)_{}`
`a_2=(12)/((3)/(24))`
`a_2=96`