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Problem 3. For each of these lists of integers provide a simple formula or rule that generates the terms of an integer sequen

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Answer #1

1:

This is a simple sequence, Every number is obtained by subtracting 7 from the previous number

a_n = a_{n-1} - 7

If we define it on the basis of the starting element 15,

then the rule is

a_n = 15 - 7*(n-1)

Next 2 terms:

given,a_7 = -27

a8 = 15 _ 7 * (8-1)=15 _ 7 * 7-15-49 -34

a9 15 _ 7 * 8 15-56 =-41

2:

The sequence here is:

a_n = 2 * ({n+1})^{3}

given,a_7=686

a_8 = 2 * (8+1)^3 = 2*9^3 = 2*729 =1458

a_9 = 2 * (9+1)^3 = 2*10^3 = 2*1000 =2000

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