Answer:
[tex]r = 0.8903 [/tex]
Step-by-step explanation:
given,
a₂ = 495
a₆ = 311
geometric sequence formula
[tex]a_n = ar^{n-1}[/tex]
[tex]a_2 = ar^{2-1}[/tex]
[tex]a_2 = ar [/tex]...................(1)
[tex]a_6 = ar^{6-1}[/tex]
[tex]a_6 = ar^5 [/tex]................(2)
dividing equation (2) by (1)
[tex]\dfrac{a_6}{a_2} = \dfrac{ar^5}{ar}[/tex]
[tex]\dfrac{311}{495} = r^4[/tex]
[tex]r^4 = 0.628 [/tex]
[tex]r = 0.8903 [/tex]
hence, the common ratio of the geometric sequence is [tex]r = 0.8903 [/tex]
