Question

What is the value of the fourth term in a geometric sequence for which a1 = 30 and r = 1/2?

Answer 1

Answer:  The required fourth term of the geometric sequence is $\dfrac{10}{9}.$

Step-by-step explanation:  We are given to find the value of the fourth term in a geometric sequence with first term and common ratio as follows :

$a(1)=30,~~~~~r=\dfrac{1}{2}.$

We know that

the n-th term of a geometric sequence with first term a1 and common ratio r given by

$a(n)=a(1)r^{n-1}.$

Therefore, the fourth term of the given geometric sequence will be

$a(4)=a(1)r^{4-1}=30\times r^3=30\times\left(\dfrac{1}{3}\right)^3=\dfrac{30}{27}=\dfrac{10}{9}.$

Thus, the required fourth term of the geometric sequence is $\dfrac{10}{9}.$

Answer 2

$\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ n=4\\ a_1=30\\ r=\frac{1}{2} \end{cases}\implies a_4=30\left( \frac{1}{2} \right)^{4-1}$