Question

50 Points! Multiple choice algebra question. Photo attached. Thank you!

Answer 1

B)

Explanation:

Geometric mean:

`\sf 5 , a_2,a_3, a_4, a_5,1215`

`\bf a_1 = first \ term = 5`

n = number of terms = 6

r = common ratio

`\boxed{\bf a_n = a_1 * r^(n-1)}`

`a^(6) = 5 *r^(6-1)\\\\1215 = 5*r^5\\\\ (1215)/(5)=r^5\\\\243=r^5\\\\3^5=r^5`

As powers are same, compare the bases,

r = 3

Each term is obtained by multiplying the previous term by the common ratio. r = 3

`\sf a_2 = 5*3 = 15\\\\a_3= 15*3 = 45\\\\a_4 = 45 *3 =135\\\\ a_5 = 135*3 = 405`