What is the 9th term of the sequence? 3,-12,48,-192, A. 786,432 B. -196,608 C. -786,432 D. 196,608

Question

asked Nov 21, 2020 117k views

2 Answers

Obdulia · Answer 1 · 2020-11-26T18:26:48+0000

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

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

So, we get

(a(2))/(a(1))=(a(3))/(a(2))=(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*(-4)^8=3* 65536=196608.

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

Option (D) is CORRECT.