Question

3. For each of the following lists of integers, provide a simple formula or rule.. Assuming that your formula or rule is correct, determine the next three term of the sequence. 15, 20, 25, 30, 35,... a. b. 5,9, 13, 17, 21, ...

Answer 1

Explanation:

Consider the first sequence:

15, 20, 25, 30, 35,...

Note that each term is increased by 5 from its previous term.

Therefore,

`a_n=a_(n-1)+5`

If the pattern continue, the next three term of the sequence will be:

`a_6=a_(6-1)+5`

`a_6=a_(5)+5`

`a_6=35+5`

`a_6=40`

Similarly,

`a_7=a_(7-1)+5`

`a_7=a_(6)+5`

`a_7=40+5`

`a_7=45`

Similarly,

`a_8=a_(8-1)+5`

`a_8=a_(7)+5`

`a_8=45+5`

`a_8=50`

Thus, the next three term of the sequence 15, 20, 25, 30, 35,... is 40, 45, and 50.

Now, consider the second sequence:

5, 9, 13, 17, 21,...

Note that each term is increased by 4 from its previous term.

Therefore,

`a_n=a_(n-1)+4`

If the pattern continue, the next three term of the sequence will be:

`a_6=a_(6-1)+4`

`a_6=a_(5)+4`

`a_6=21+4`

`a_6=25`

Similarly,

`a_7=a_(7-1)+4`

`a_7=a_(6)+4`

`a_7=25+4`

`a_7=29`

Similarly,

`a_8=a_(8-1)+4`

`a_8=a_(7)+4`

`a_8=29+4`

`a_8=33`

Thus, the next three term of the sequence 5, 9, 13, 17, 21,... is 25, 29, and 33.