QUESTION 7 Look at this sequence $$ 3 ; 6 ; 11 ; 18 ; 27 ; \ldots ; \ldots ; $$ 7.1. Write the next 2 terms 7.2. In the pattern $$ 7 ; 11 ; 15 ; 19 ; \ldots ; $$ 7.2.1. Find the constant difference 7.2.2. Describe the patterns in your own

Question

UpStudy AI · Accepted Answer

**7.1. Next Two Terms of the Sequence**

The given sequence is:  
$$
3,\; 6,\; 11,\; 18,\; 27,\; \ldots
$$

1. First, calculate the differences between consecutive terms:
   - $$6 - 3 = 3$$
   - $$11 - 6 = 5$$
   - $$18 - 11 = 7$$
   - $$27 - 18 = 9$$

2. Notice that the differences form the sequence:  
   $$
   3,\; 5,\; 7,\; 9,\; \ldots
   $$
   Each difference increases by $$2$$.

3. To find the next term, add the next expected difference:
   - Next difference: $$9 + 2 = 11$$
   - Next term: $$27 + 11 = 38$$

4. For the following term:
   - Next difference after $$11$$: $$11 + 2 = 13$$
   - Next term: $$38 + 13 = 51$$

Thus, the next two terms in the sequence are:  
$$
38 \quad \text{and} \quad 51
$$

---

**7.2. Analysis of the Pattern $$7 ; 11 ; 15 ; 19 ; \ldots$$**

**7.2.1. Finding the Constant Difference**

1. Calculate the differences:
   - $$11 - 7 = 4$$
   - $$15 - 11 = 4$$
   - $$19 - 15 = 4$$

The constant difference is:  
$$
4
$$

**7.2.2. Describing the Pattern**

This pattern is an arithmetic sequence since the difference between any two consecutive terms is constant. Each term increases by $$4$$ from the previous term. In general, an arithmetic sequence can be written using the formula:
$$
a_n = a_1 + (n-1)d
$$
where $$a_1$$ is the first term and $$d$$ is the constant difference. For this sequence:
- $$a_1 = 7$$
- $$d = 4$$

Thus, each term is obtained by adding $$4$$ to the term before it, creating a steady and predictable progression.
**7.1. Next Two Terms of the Sequence** The next two terms are **38** and **51**. **7.2. Analysis of the Pattern $$7 ; 11 ; 15 ; 19 ; \ldots$$** **7.2.1. Constant Difference** The constant difference is **4**. **7.2.2. Pattern Description** This is an arithmetic sequence where each term increases by **4**.

QUESTION 7 Look at this sequence \( 3 ; 6 ; 11 ; 18 ; 27 ; \ldots ; \ldots ; \) 7.1. Write the next 2 terms 7.2. In the pattern \( 7 ; 11 ; 15 ; 19 ; \ldots ; \) 7.2.1. Find the constant difference 7.2.2. Describe the patterns in your own

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Arithmetic Questions