Question

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

Answer 1

`\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=(1)/(2) \end{cases}\implies a_4=30\left( (1)/(2) \right)^(4-1)`

Answer 2

Answer: The required fourth term of the geometric sequence is
`(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=(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* r^3=30*\left((1)/(3)\right)^3=(30)/(27)=(10)/(9).`

Thus, the required fourth term of the geometric sequence is
`(10)/(9).`