Question

Complete the recursive formula of the geometric sequence 27,,-9,3-1,...

b(1)=
b(n)=b(n−1)⋅

Answer 1

b(1)= 27

b(n)=b(n-1)• -1/3

Explanation:

answer on khan

Answer 2

The recursive formula of the geometric sequence is:

• aₙ = aₙ₋₁ (r)

Explanation:

A recursive formula is a formula using which every next term is based on the previous term.

Each next term of a geometric sequence can be determined when we multiply the previous term with a constant. That constant number is called a 'common ratio' which is denoted by 'r'.

Given the sequence

27, -9, 3, -1,...

Let us find the common ratio 'r' of all the adjacent terms

r = -9/27 = -1/3, r = 3/-9 = -1/3, r = -1/3

Thus, the common ratio is: r= -1/3

The recursive formula for the geometric sequence is:

aₙ = aₙ₋₁ (r)

Here,

aₙ represents the general term

aₙ₋₁ represents the previous term

'r' represents the common ratio

as

a₁ = 27

Substituting our values, we have

aₙ=aₙ₋₁(r)

Putting n=2 to get the second value

a₂=a₂₋₁(-1/3)

= a₁ (-1/3)

= 27 (-1/3)

= -9

Thus, the next term of a geometric sequence can be determined when we multiply the previous term with a constant.

Therefore, the recursive formula of the geometric sequence is:

• aₙ = aₙ₋₁ (r)