Question

consider the sequence with first term 2 and second term 4. if these are the first two terms of a geometric sequence, what is the third term? 6 8 16 there is not enough information to determine the third term in the sequence.

Explanation:

Step1: Find the common ratio

In a geometric sequence, the common ratio $r$ is given by $r=\frac{a_{2}}{a_{1}}$. Here, $a_{1} = 2$ and $a_{2}=4$, so $r=\frac{4}{2}=2$.

Step2: Calculate the third - term

The formula for the $n$th term of a geometric sequence is $a_{n}=a_{1}r^{n - 1}$. For the third term ($n = 3$), $a_{3}=a_{1}r^{2}$. Substituting $a_{1}=2$ and $r = 2$ into the formula, we get $a_{3}=2\times2^{2}=2\times4 = 8$.

Answer:

8