Question

.............................

Answer 1

xy23 x xy23 . multiple it

Answer 2

`a_n=281.25 \cdot 0.8^(n-1)`

or
`a_n=281.3 \cdot 0.8^(n-1)` (with a rounded to the nearest tenth)

Explanation:

Geometric sequence formula:
`a_n=ar^(n-1)`

(where
`a` is the initial term and
`r` is the common ratio)

Given:

• 
  `a_3=180`
• 
  `a_5=115.2`

`\implies a_3=ar^(2)=180`

`\implies a_5=ar^(4)=115.2`

Common ratio r

`(ar^4)/(ar^2)=(115.2)/(180)`

`\implies r^2=0.64`

`\implies r=√(0.64)`

`\implies r=0.8`

Initial term a:

`\implies a\cdot 0.8^(2)=180`

`\implies a=281.25`

Final equation

`a_n=281.25\cdot 0.8^(n-1)`