Question

Algebra i P.1 Identify arithmetic and geometric sequences X76 You have prizes to re Farmer Hanson has a plot of tomato plants. There are 2 tomato plants in the first row, 8 tomato plants in the second row, 32 tomato plants in the third row, and 128 tomato plants in the fourth row. What kind of sequence is this? arithmetic geometric both neither Submit ​

Answer 1

Answer: Geometric

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Step-by-step explanation:

The sequence 2,8,32,128,... is geometric

To get a new term, we multiply by the common ratio 4.

2*4 = 8

8*4 = 32

32*4 = 128

To find the common ratio, you pick any term you want, and divide by its previous term

r = (term2)/(term1) = 8/2 = 4

r = (term3)/(term2) = 32/8 = 4

r = (term4)/(term3) = 128/32 = 4

The starting term is a = 2, so the nth term is

a(n) = a*(r)^(n-1)

a(n) = 2*(4)^(n-1)