Question

A sequence has a first term of 2 and a constant ratio of -2/3. What are the first five toerms of the sequence?

Answer 1

`a_1=2;\ r=-(2)/(3)\ therefore\ a_n=2\cdot\left(-(2)/(3)\right)^(n-1)\\\\a_1=2\\\\a_2=2\cdot\left(-(2)/(3)\right)=-(4)/(3)\\\\a_3=2\cdot\left(-(2)/(3)\right)^2=2\cdot(4)/(9)=(8)/(9)\\\\a_4=2\cdot\left(-(2)/(3)\right)^3=2\cdot\left(-(8)/(27)\right)=-(16)/(27)\\\\a_5=2\cdot\left(-(2)/(3)\right)^4=2\cdot(16)/(81)=(32)/(81)\\\\\vdots`