Question

How do you find the indicated term of the geometric sequence where `a_6=3`, r=2, n=12?

Answer 1

`a_12=color(red)(192)`

Explanation:

`a_6=3=a_5xxr=a_5xx2`
`color(white)("XXX") rarr 3=a_5xx2`
`color(white)("XXX") rarr a_5=3/2`

Similarly
`color(white)("XXX")a_4=3/(2^2)`
`color(white)("XXX")a_3=3/(2^3)`
`color(white)("XXX")a_2=3/(2^4)`
`color(white)("XXX")a_1=3/(2^5)`
`color(white)("XXX")a_0=3/(2^6)`

`a_n=a_0xxr^n`
`color(white)("XXX")rarr a_12=3/(2^6)xx2^12`
`color(white)("XXXXXX")=3xx2^6`
`color(white)("XXXXXX")=2xx64`
`color(white)("XXXXXX")=192`