FIRST TERMS OF GEOMETRIC SEQUENCE 160 80 40WHAT WOULD THE NEXT TWO SEQUENCE BE? N COULD U TELL ME HOW TO YOU GOT THE SEQUENCES?

Answer:The next two terms of the sequence are 20, 10 Solution: The geometric equation is 160, 80, 40….. The first term of the equation is[tex]a_{1}=160[/tex]. Now the ratio between the numbers of the sequence [tex]r=\left(\frac{80}{160}\right)=\left(\frac{1}{2}\right)[/tex]As we know that the nth term of the sequence [tex]a_{n}=a_{1} \times r^{n-1}[/tex]Hence,  [tex]a_{4}=160 \times\left(\frac{1}{2}\right)^{4-1}[/tex][tex]\rightarrow 160 \times\left(\frac{1}{2}\right)^{3}[/tex] [tex]\rightarrow160 \times\left(\frac{1}{8}\right) = 20[/tex][tex]\mathrm{a}_{5}=160 \times\left(\frac{1}{2}\right)^{5-1}[/tex][tex]\rightarrow160 \times\left(\frac{1}{2}\right)^{4}[/tex][tex]\rightarrow160 \times\left(\frac{1}{16}\right) = 10[/tex]