Question

In a certain sequence, each term, starting with the 3rd term, is found by multiplying the previous two terms. What is the difference between the 6th and 3rd terms in the sequence

Answer 1

Answer:

-3

Step-by-step explanation:

Let the first term be a-d, second term be a and third term be a+d

d is the common difference

If each term, starting with the 3rd term, is found by multiplying the previous two terms then:

a(a-d) = a+d

a²+ad-a-d = 0

a(a+d)-1(a+d) = 0

(a+d)(a-1) = 0

a-1 = 0

a= 1

a+d = 0

1+d = 0

d = 0-1

d = -1

Get the sixth term

nth term of a sequence is expressed as

Tn = a+(n-1)d

T6 = 1+(6-1)(-1)

T6 = 1+5(-1)

T6 = 1-5

T6 = -4

Get the third term T3

T3 = a+2d

T3 = 1+2(-1)

T3 = 1-2

T3 = -1

difference between the 6th and 3rd terms in the sequence is expressed as;

Difference = T6-T3

Difference = -4-(-1)

Difference = -4+1

Difference = -3