Question

Burak received 12 rare stamps as a gift from his grandfather, so he decided to start a stamp collection.
From the following week onward, Burak added 4 new stamps to his collection each week.
Let g(n) be the total number of stamps in Burak's collection in the nth week of the collection.
g is a sequence. What kind of sequence is it?

Answer 1

Answer:

It is an Arithmetic Sequence.

g(1)= 12

g(n)=g(n-1) + 4

Step-by-step explanation:

Let's consider the first three terms of g(n) to get a sense of how the function values change as n increases.

The first term is the size of Burak's collection in the first week, which is the 12 stamps he received from his grandfather.

The second term is the size of Burak's collection in the second week. Since he added 4 stamps to the collection each week, the second term is 12+4=16 stamps.

The third term is the size of Burak's collection in the third week. Again, this is

4 stamps more than one week earlier, so the third term is 16+4=20 stamps.

To summarize:

• g(1)=12
• g(2)=12+4
• g(3)=12+4+4

We can see that each term is 4 more than its preceding term. There is a constant difference between consecutive terms. Therefore, this is an arithmetic sequence.

Let's find a recursive formula for g(n)

• The first term is the initial size of the collection, which is 12 stamps.
• The common difference is the amount Burak added each week, which is 4 stamps.

Therefore, this is the recursive definition of the sequence:

g(1)=12

g(n)=g(n−1)+4

In conclusion, g is an arithmetic sequence.

g(1)=12

g(n)=g(n−1)+4

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