1 Answer

Asef Hossini · Answer 1 · 2023-11-20T12:32:40+0000

Answer:

$a_1=759,375;\text{ }a_n=a_(n-1)\cdot(1)/(15)$

The nth term of a geometric sequence is given as:

where:

a is the first term

r is the common ratio

If two terms in a geometric sequence are a₅ = 15 and a₆ = 1, then;

$\begin{gathered} a_5=ar^(5-1) \\ ar^4=15 \end{gathered}$

Similarly;

$\begin{gathered} a_6=ar^(6-1) \\ 1=ar^5 \end{gathered}$

Take the ratio of both expressions to get the common ratio "r"

$\begin{gathered} (ar^5)/(ar^4)=(1)/(15) \\ r=(1)/(15) \end{gathered}$

The standard recursive function is given as:

$a_n=r\cdot a_(n-1)$

Substitute the value for the common ratio to have;

$a_n=(1)/(15)\cdot a_(n-1)$

To get the first term a₁, we will use the equivalent nth term of the sequence above

$\begin{gathered} \\ a_n=ar^(n-1) \\ a_5=ar^4 \\ 15=a((1)/(15))^4 \\ 15=a((1)/(50,625)) \\ a=15*50,625 \\ a=759,375 \end{gathered}$

Hence the first term of the sequence is 759,375