Question

If a geometric sequence has a2 = 495 and a6 = 311, approximate the value of the common ratio ???? to four decimal

Answer 1

Answer:

$r = 0.8903$

Step-by-step explanation:

given,

a₂ = 495

a₆ = 311

geometric  sequence formula

                       $a_n = ar^{n-1}$

                       $a_2 = ar^{2-1}$

                       $a_2 = ar$...................(1)

                       $a_6 = ar^{6-1}$

                       $a_6 = ar^5$................(2)

dividing equation (2) by (1)

                     $\dfrac{a_6}{a_2} = \dfrac{ar^5}{ar}$

                     $\dfrac{311}{495} = r^4$

                     $r^4 = 0.628$

                     $r = 0.8903$

hence, the common ratio of the geometric sequence is $r = 0.8903$