Question

What is the 9th term of the sequence? 3,-12,48,-192,

Answer 1

D, 196,608.

The sequence is multiplying by -4 every time.

Answer 2

Answer:  The correct option is (D) 196608.

Step-by-step explanation:  We are given to find the 9th term of the following sequence :

3,    -12,    48,    -192,    .    .    .

Let a(n) denote the n-th term of the given sequence.

Then, a(1) = 3,  a(2) = -12,  a(3) = 48,  a(4) = -192,   .   .   .

We see that

$\dfrac{a(2)}{a(1)}=\dfrac{-12}{3}=-4,\\\\\\\dfrac{a(3)}{a(2)}=\dfrac{48}{-12}=-4,\\\\\\\dfrac{a(4)}{a(3)}=\dfrac{-192}{48}=-4,~~.~~.~~.$

So, we get

$\dfrac{a(2)}{a(1)}=\dfrac{a(3)}{a(2)}=\dfrac{a(4)}{a(3)}=~~.~~.~~.~~=-4.$

That is, the given sequence is a GEOMETRIC one with first term a = 3  and common ratio d= -4.

We know that

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

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

Therefore, the 9th term of the given sequence is

$a(9)=ar^{9-1}=3\times(-4)^8=3\times 65536=196608.$

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

Option (D) is CORRECT.