Question

Write an explicit rule for the recursive rule. a1=−2,an=9an−1

Answer 1

`a_n=-2\cdot 9^(n-1).`

Explanation:

You are given that

• 
  `a_1=-2;`
• 
  `a_n=9a_(n-1).`

Then

`a_1=-2,\\ \\a_2=9a_1=9\cdot (-2)=-18,\\ \\a_3=9a_2=9\cdot (-18)=-162, \dots`

Actually, this sequence is the geometric seequence with first term
`a_1=-2` and ratio
`r=9.`

The explicit rule for the nth term of the geometric sequence is

`a_n=a_1\cdot r^(n-1).`

Hence,

`a_n=-2\cdot 9^(n-1).`