Question

Find the next three terms in the geometric sequence. Write any terms as fractions, if necessary. 36, 12, 4, ...

Answer 1

36, 12, 4, (4/3), (4/9), (4/27)

Step-by-step explanation

Geometric sequence is one in which each term is obtained by multiplying or dividing a constant to the preceding term.

The nth term of a geometric sequence is given as

aₙ = a rⁿ⁻¹

`a_n=a(r^(n-1))`

where

a = first term = 36

n = number of terms

r = common ratio = (Second term)/(First term) = (Third term)/(Second term)

r = (12/36) = (4/12) = ⅓

So, we can find the next three terms.

Fourth term,

a = 36

n = 4

r = ⅓

`\begin{gathered} a_n=a(r^(n-1)) \\ a_4=36\lbrack((1)/(3))^(4-1)\rbrack \\ a_4=36\lbrack((1)/(3))^3\rbrack \\ a_4=36((1)/(27))=(36)/(27)=(4)/(3) \end{gathered}`

For the fifth and sixth term, we can just keep multiplying by the common ratio, ⅓

Fourth term = (4/3)

Fifth term = (4/3) × (1/3) = (4/9)

Sixth term = (4/9) × (1/3) = (4/27)

Hope this Helps!!!