Question

A sequence is defined by the following:

A1 = 6 and an = -1.2n-1
What is the 4th term?
-12.4416
-10.368
10.368
12.4416

Answer 1

Explanation:

a1 = 6

a2 = -1.2*a_(n-1)

a2 = -1.2*a_1

a2 = -1.2 * 6

a2 = -7.2

a3 = -1.2*a_(n-1)

a3 = -1.2*a_2

a3 = -1.2 * - 7.2

a3 = 8.64

a4 = -1.2 * a_3

a4 = -1.2 * 8.64

a4 = -10.368

Answer 2

Answer: The correct option is (B) -10.368.

Step-by-step explanation: Given that a sequence is defined b the following :

`a_1=6,~~~a_n=-1.2a_(n-1).`

We are to find the 4-th term.

To find the fourth term, we need to start from finding the first term.

If n = 2, then the second term is given by

`a_2=-1.2* a_1=-1.2* 6=-7.2.`

If n = 3, then the third term is given by

`a_3=-1.2* a_2=-1.2* (-7.2)=8.64.`

If n = 4, then the fourth term is given by

`a_4=-1.2* a_3=-1.2* 8.64=-10.368.`

Thus, the fourth term of the given sequence is -10.368.

Option (B) is CORRECT.