Angela opened a new bakery. she got orders for 2 cakes the first week, 4 cakes the second week, and 8 cakes the third week. if the pattern continues, how many cake orders will angela get the fourth week. show your work and explain the answer

She will get 16 cakes order the fourth week.

Step-by-step explanation:

The sequence depicts a geometric progression. A geometric progression is a sequence whereby each term after the first element is gotten by multiplying the previous term with a common ratio.

The first week she ordered 2 cakes, the second week she ordered 4 cakes and the third week she ordered 8 cakes. The pattern is a geometric progression. Let the sequence be represented as 2, 4, 8 .  

Using geometric progression formula the number of cake she ordered on the 4th week can be computed as ar∧ n-1 .

where a = first term

r = common ratio

n = number of terms

ar∧ n-1

a = 2

r = 2

n = 4 (Note we are looking for the 4th term)

2 × 2∧ 4-1

2 × 2∧ 3

2 × 8

16

answer: for each 3 girls there is 2 boys . 3: 2

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