Question

Please someone help me with this

Answer 1

Answer: 2.703

Work Shown

This sequence appears to be geometric. Let's test that claim. We divide each term over its previous term:

• r = term2/term1 = 27/36 = 3/4
• r = term3/term2 = (81/4) /27 = (81/4)*(1/27) = 3/4

The sequence is geometric. The common ratio is r = 3/4 = 0.75

The first term is a = 36

The nth term goes from the template
`a_n = a*(r)^(n-1)` to
`a_n = 36*\left((3)/(4)\right)^(n-1)`

Next we plug n = 10 into this equation to find the tenth term.

`a_n = 36*\left((3)/(4)\right)^(n-1)\\\\a_(10) = 36*\left((3)/(4)\right)^(10-1)\\\\a_(10) \approx 2.7030487\\\\a_(10) \approx 2.703\\\\`

The tenth term is approximately 2.703