401/HK17. problem / Math - Solved Math Problems

MR-401 / 2. problem

The second member of a geometric series is 6, the third member is 18. Enter the fifth member of the series!

Source: Magyarország: Unified final exam for high schools - Mathematics - intermediate level [09.05.2017.] - 2..)

Algebra → Exponential equations and inequalities → Exponential equations

a_{2} = 6; a_{3} = - 18

q = \frac{a_{3}}{a_{2}} = \frac{- 18}{6}

q = - 3

a_{2} = a_{1} \cdot q

6 = a_{1} \cdot (- 3)

a_{1} = \frac{6}{- 3}

a_{1} = - 2

a_{n} = a_{1} \cdot q^{n - 1}

a_{5} = a_{1} \cdot q^{5 - 1} = (- 2) \cdot {(- 3)}^{4} = (- 2) \cdot 81

a_{5} = - 162

a_{5} = - 162