Question

For a geometric sequence, t8 = 60 and t6 = 72, how do you find t10?

Answer 1

`T_10=50`

Explanation:

The general formula for the `nth` term in a geometric sequence is this: `T_n=ar^(n-1)`
`T_8=ar^7=60`
`T_6=ar^5=72`, and know we have to solve for `r`, and we can do this by using the two information we have:
`T_8/T_6=60/72=(ar^7)/(ar^5)=r^2`
`60/72=r^2`
`5/6=r^2`
As you'll see, we don't need to square root `r^2`:
`T_10=ar^9`
`=ar^7*r^2`
`=T_8*r^2`
`=60*5/6`
`=50`