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

-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

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