Question

What is the value of the 9th term in the following geometric sequence?

Answer 1

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 that

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

$a_n=ar^{n-1}.$

For the given sequence, we have

first term, a = 3  and the common ratio, r is given by

$r=\dfrac{12}{3}=\dfrac{48}{12}=\dfrac{192}{48}=~~.~~.~~.~~=4.$

Therefore, the 9th term of the given sequence will be

$a_9=ar^{9-1}=3\times 4^8=3\times65536=196608.$

Thus, the required 9th term of the given sequence is 196608.

Option (D) is CORRECT.