Question

5.) Digger the Dog saves the same number of bones each week.

What type of sequence represents his total number of saved bones? How can you tell?
b. After week 4, he had 23 bones, and after week 8, he had 35 bones. How many did he start
with? Show your table and general rule.

Answer 1

(a) ARITHMETIC SEQUENCE represents his total number of saved bones.

(b) Dog initially started with 11 bones.

General Term for bones saved in n weeks = 11 + 3 n

Explanation:

Digger the dog saves the same number of bones each week.

Let us assume the number of bones saved by dog each week = m

So, here the number of bones saved in:

First week = m, Second week = m + m = 2 m, Third week = m + m + m = 3 m

and so on..

(a) The sequence represented is m, 2 m, 3 m , ...

Since here each term is 'm' MORE than the previous term , the given sequence is an ARITHMETIC SEQUENCE with common ration as m.

(b) After week 4, he had 23 bones.

After 8 weeks he had 35 bones.

Let us assume he started with k bones.

So, the bones he has after 4 weeks

= 4 ( bones saved first week) + Initial bones = 4 m + a

⇒ 4 m + a = 23 ... (1)

Similarly, bones he has after 8 weeks

= 8 ( bones saved first week) + Initial bones = 8 m + a

⇒ 8 m + a = 35 ... (2)

Solving (1) and (2) , we get:

m = 3, a = 11

So the GENERAL rule for n weeks = a + n m = 11 + 3 n

Hence the dog initially had 11 bones and he saved 3 bones per week.