Question

31. (05.08 MC)

What is the equation for a geometric sequence with a first term of 3 and a second term of -9?

Answer 1

`a_n=3(-3)^(n-1)`

Explanation:

Geometric sequence

General form of a geometric sequence:
`a_n=ar^(n-1)`

where:

• 
  `a_n` is the nth term
• a is the first term
• r is the common ratio

Given:

• 
  `a_1=3`
• 
  `a_2=-9`

To find the common ratio r, divide consecutive terms:

`\implies r=(a_2)/(a_1)=(-9)/(3)=-3`

Therefore, the equation is:

`a_n=3(-3)^(n-1)`