Question

Given the term in a geometric sequence and the common ratio find the explicit formula

Answer 1

Step-by-step explanation

Given that

`\begin{gathered} second\text{ term=}a_2=12 \\ common\text{ }ratio=-6 \end{gathered}`

We know that the second term can be defined as;

`\begin{gathered} a_2=a_1r \\ where\text{ a}_1is\text{ the first term of the geometric sequence.} \\ Therefore,\text{ when we substitute the given values, we will have;} \\ 12=a_1(-6) \\ Divide\text{ both sides by -6} \\ a_1=(12)/(-6)=-2 \end{gathered}`

Having derived the value of the first term, we can now find the explicit formula as

`\begin{gathered} a_n=a_1r^(n-1) \\ since\text{ a}_1=-2\text{ and r=-6} \\ therefore; \\ a_n=-2(-6)^(n-1) \end{gathered}`

Answer: Option b