Question

A geometric series has second term

375 and fifth term 81. The nth term
of the series is Un. Find the value of
un
n = 6

Answer 1

Answer: 243/5 = 48.6

Explanation:

a₁, 375, a₃, a₄, 81 , a₆

First, let's find the ratio (r). There are three multiple from 375 to 81.

`375r^3=81\\\\r^3=(81)/(375)\\\\\\r^3=(27)/(125)\qquad \leftarrow simplied\\\\\\\sqrt[3]{r^3} =\sqrt[3]{(27)/(125)}\\ \\\\r=(3)/(5)`

Next, let's find a₆ which is one multiple from 81.

`a_6=81\bigg((3)/(5)\bigg)^1\\\\\\.\quad =\large\boxed{(243)/(5)}`