Question

Which of the following explicit equations represents the sequences -5,10,20,40 EXPLAIN PLSS

Answer 1

we have the sequence

5,10,20,40,...

so

a1=5 ----> first term

a2=10

a3=20

a4=40

a2/a1=10/5=2

a3/a2=20/10=2

a4/a3=40/20=2

we have a geometric sequence with a common ratio r=2

the equation is of the form

$r(n)=a_1\cdot r^{(n-1)}$

substitute given values

$\begin{gathered} r(n)=5\cdot2^{(n-1)} \\ r(n)=5\cdot2^n\cdot2^{-1} \\ r(n)=5\cdot2^n\cdot\frac{1}{2} \\ r(n)=2.5\cdot2^n^{} \end{gathered}$

the answer is the first option