Question

Erica is studying two number patterns. Pattern A starts at 0 and has the rule "add 5." Pattern B starts at 0 and has the rule "add 10." What is the relationship between corresponding terms in the two patterns? The terms in Pattern B are 5 times the corresponding terms in Pattern A. The terms in Pattern B are 2 times the corresponding terms in Pattern A. The terms in Pattern B are one half the corresponding terms in Pattern A. The terms in Pattern B are one fifth the corresponding terms in Pattern A.

Answer 1

The terms in Pattern B are 2 times the corresponding terms in Pattern A

Explanation:

Given

Pattern A

`Start = 0`

`Rule: Add\ 5`

Pattern B

`Start = 0`

`Rule: Add\ 10`

Required

The relationship between both patterns

First, we calculate the nth term of both pattern.

For A

`A(n) = Start + Rule`

`A(n) = 0 + 5n`

`A(n) = 5n`

For B

`B(n) = Start + Rule`

`B(n) = 0 + 10n`

`B(n) = 10n`

So, we have:

`A(n) = 5n`

`B(n) = 10n`

B(n) can be expressed as:

`B(n)=2* 5n`

Substitute
`A(n) = 5n`

`B(n)=2* A(n)`

This means that the term of B(n) is twice the corresponding term of A(n)