How do you find the missing parts of the geometric sequence: 2.5, , , , 202.5?

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Answer 1 · 2018-03-22T09:14:15

The Geometric sequence is #color(green)(2.5), color(blue)(7.5, 22.5, 67.5), color(green)(202.5,. . . #

Given : #a_1 = 2.5, a_5 = 202.5, " To find " a_2, a_3, a_4#

#n^(th) " term " a_n = a_1 r^(n-1)# where r is the common ratio.

#a_5 / a_1 = 202.5 / 2.5 (cancel(a_1) r^(5-1))/cancel(a_1)#

#r^4 = cancel(202.5)^color(red)(81) / cancel 2.5#

#r^4 = 81 = (3)^4 , or r = 3#

#a_2 = a_1 * r(2-1) = a_1 * r = 2.5 * 3 = 7.5#

#a_3 = a_1 * r(3-1) = 2.5 * 3^2 = 22.5#

@a_4 = a_3 * r = 22.5 * 3 = 67.#