What is the value of the 9th term in the following geometric sequence?3, 12, 48, 192, ...A. 96B. 786,429C. 105D. 196,608

Answer:  The correct option is (D) 196608.Step-by-step explanation:  We are given to find the value of the 9th term in the following geometric sequence :3,     12,    48,    192,    .     .     .We know thatthe n-th term of a geometric sequence with first term a and common ratio r is given by[tex]a_n=ar^{n-1}.[/tex]For the given sequence, we havefirst term, a = 3  and the common ratio, r is given by[tex]r=\dfrac{12}{3}=\dfrac{48}{12}=\dfrac{192}{48}=~~.~~.~~.~~=4.[/tex]Therefore, the 9th term of the given sequence will be[tex]a_9=ar^{9-1}=3\times 4^8=3\times65536=196608.[/tex]Thus, the required 9th term of the given sequence is 196608.Option (D) is CORRECT.