1. Write down the next four terms of each $$ \begin{array}{lll} ext { (i) } 3,5,7,9,11, \ldots & ext { (ii) } 2,5,8,11,14, \ldots & ext { (iii) } 4,8,12,16,20, \ldots \ ext { (iv) } 20,18,16,14, \ldots & ext { (v) } 50,45,40,35, \ldots & ext { (vi) } 12,8,4, \ldots\end{array} $$ 2. Write down the next three terms of each of these sequences: $$ \begin{array}{lll} ext { (i) } 1,1.5,2,2.5, \ldots & ext { (ii) }-10,-8,-6,-4, \ldots & ext { (iii) } 2,6,18,54, \ldots \ ext { (iv) }-\frac{1}{2}, 1,2 \frac{1}{2}, 4, \ldots & ext { (v) }-40,-20,-10, \ldots & ext { (vi) } 6,3,0, \ldots\end{array} $$

Question

1. Write down the next four terms of each $$ \begin{array}{lll}	ext { (i) } 3,5,7,9,11, \ldots & 	ext { (ii) } 2,5,8,11,14, \ldots & 	ext { (iii) } 4,8,12,16,20, \ldots \ 	ext { (iv) } 20,18,16,14, \ldots & 	ext { (v) } 50,45,40,35, \ldots & 	ext { (vi) } 12,8,4, \ldots\end{array} $$ 2. Write down the next three terms of each of these sequences: $$ \begin{array}{lll}	ext { (i) } 1,1.5,2,2.5, \ldots & 	ext { (ii) }-10,-8,-6,-4, \ldots & 	ext { (iii) } 2,6,18,54, \ldots \ 	ext { (iv) }-\frac{1}{2}, 1,2 \frac{1}{2}, 4, \ldots & 	ext { (v) }-40,-20,-10, \ldots & 	ext { (vi) } 6,3,0, \ldots\end{array} $$

UpStudy AI · Accepted Answer

Sure, let's address each part of your questions step by step.

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### **1. Write down the next four terms of each sequence:**

#### **(i) $$3, 5, 7, 9, 11, \ldots$$**

- **Pattern:** This is an arithmetic sequence where each term increases by **2**.
  
- **Next four terms:**
  - $$13$$ (11 + 2)
  - $$15$$ (13 + 2)
  - $$17$$ (15 + 2)
  - $$19$$ (17 + 2)

- **Sequence with next terms:** $$3, 5, 7, 9, 11, \mathbf{13, \, 15, \, 17, \, 19}$$

---

#### **(ii) $$2, 5, 8, 11, 14, \ldots$$**

- **Pattern:** This is an arithmetic sequence with a common difference of **3**.

- **Next four terms:**
  - $$17$$ (14 + 3)
  - $$20$$ (17 + 3)
  - $$23$$ (20 + 3)
  - $$26$$ (23 + 3)

- **Sequence with next terms:** $$2, 5, 8, 11, 14, \mathbf{17, \, 20, \, 23, \, 26}$$

---

#### **(iii) $$4, 8, 12, 16, 20, \ldots$$**

- **Pattern:** This is an arithmetic sequence where each term increases by **4**.

- **Next four terms:**
  - $$24$$ (20 + 4)
  - $$28$$ (24 + 4)
  - $$32$$ (28 + 4)
  - $$36$$ (32 + 4)

- **Sequence with next terms:** $$4, 8, 12, 16, 20, \mathbf{24, \, 28, \, 32, \, 36}$$

---

#### **(iv) $$20, 18, 16, 14, \ldots$$**

- **Pattern:** This is an arithmetic sequence with a common difference of **-2** (decreasing by 2).

- **Next four terms:**
  - $$12$$ (14 - 2)
  - $$10$$ (12 - 2)
  - $$8$$ (10 - 2)
  - $$6$$ (8 - 2)

- **Sequence with next terms:** $$20, 18, 16, 14, \mathbf{12, \, 10, \, 8, \, 6}$$

---

#### **(v) $$50, 45, 40, 35, \ldots$$**

- **Pattern:** This is an arithmetic sequence where each term decreases by **5**.

- **Next four terms:**
  - $$30$$ (35 - 5)
  - $$25$$ (30 - 5)
  - $$20$$ (25 - 5)
  - $$15$$ (20 - 5)

- **Sequence with next terms:** $$50, 45, 40, 35, \mathbf{30, \, 25, \, 20, \, 15}$$

---

#### **(vi) $$12, 8, 4, \ldots$$**

- **Pattern:** This is an arithmetic sequence with a common difference of **-4** (decreasing by 4).

- **Next four terms:**
  - $$0$$ (4 - 4)
  - $$-4$$ (0 - 4)
  - $$-8$$ (-4 - 4)
  - $$-12$$ (-8 - 4)

- **Sequence with next terms:** $$12, 8, 4, \mathbf{0, \, -4, \, -8, \, -12}$$

---

### **2. Write down the next three terms of each sequence:**

#### **(i) $$1, 1.5, 2, 2.5, \ldots$$**

- **Pattern:** This is an arithmetic sequence with a common difference of **0.5**.

- **Next three terms:**
  - $$3$$ (2.5 + 0.5)
  - $$3.5$$ (3 + 0.5)
  - $$4$$ (3.5 + 0.5)

- **Sequence with next terms:** $$1, 1.5, 2, 2.5, \mathbf{3, \, 3.5, \, 4}$$

---

#### **(ii) $$-10, -8, -6, -4, \ldots$$**

- **Pattern:** This is an arithmetic sequence with a common difference of **2**.

- **Next three terms:**
  - $$-2$$ (-4 + 2)
  - $$0$$ (-2 + 2)
  - $$2$$ (0 + 2)

- **Sequence with next terms:** $$-10, -8, -6, -4, \mathbf{-2, \, 0, \, 2}$$

---

#### **(iii) $$2, 6, 18, 54, \ldots$$**

- **Pattern:** This is a geometric sequence where each term is multiplied by **3**.

- **Next three terms:**
  - $$162$$ (54 × 3)
  - $$486$$ (162 × 3)
  - $$1458$$ (486 × 3)

- **Sequence with next terms:** $$2, 6, 18, 54, \mathbf{162, \, 486, \, 1458}$$

---

#### **(iv) $$-\frac{1}{2}, 1, 2 \frac{1}{2}, 4, \ldots$$**

- **Pattern:** This is an arithmetic sequence with a common difference of **1.5**.

- **Next three terms:**
  - $$5.5$$ (4 + 1.5)
  - $$7$$ (5.5 + 1.5)
  - $$8.5$$ (7 + 1.5)

- **Sequence with next terms:** $$-\frac{1}{2}, 1, 2 \frac{1}{2}, 4, \mathbf{5.5, \, 7, \, 8.5}$$

---

#### **(v) $$-40, -20, -10, \ldots$$**

- **Pattern:** This sequence adds increasing increments where each difference is half of the previous difference:
  - From $$-40$$ to $$-20$$: $$+20$$
  - From $$-20$$ to $$-10$$: $$+10$$
  - Continuing this pattern, the next differences will be $$+5$$, $$+2.5$$, …

- **Next three terms:**
  - $$-5$$ (-10 + 5)
  - $$-2.5$$ (-5 + 2.5)
  - $$-1.25$$ (-2.5 + 1.25)

- **Sequence with next terms:** $$-40, -20, -10, \mathbf{-5, \, -2.5, \, -1.25}$$

---

#### **(vi) $$6, 3, 0, \ldots$$**

- **Pattern:** This is an arithmetic sequence with a common difference of **-3**.

- **Next three terms:**
  - $$-3$$ (0 - 3)
  - $$-6$$ (-3 - 3)
  - $$-9$$ (-6 - 3)

- **Sequence with next terms:** $$6, 3, 0, \mathbf{-3, \, -6, \, -9}$$

---

Feel free to ask if you need further explanations or assistance!
Here are the next terms for each sequence: 1. **(i) 3, 5, 7, 9, 11, 13, 15, 17, 19** 2. **(ii) 2, 5, 8, 11, 14, 17, 20, 23, 26** 3. **(iii) 4, 8, 12, 16, 20, 24, 28, 32, 36** 4. **(iv) 20, 18, 16, 14, 12, 10, 8, 6** 5. **(v) 50, 45, 40, 35, 30, 25, 20, 15** 6. **(vi) 12, 8, 4, 0, -4, -8, -12** --- 1. **(i) 1, 1.5, 2, 2.5, 3, 3.5, 4** 2. **(ii) -10, -8, -6, -4, -2, 0, 2** 3. **(iii) 2, 6, 18, 54, 162, 486, 1458** 4. **(iv) -1/2, 1, 2 1/2, 4, 5.5, 7, 8.5** 5. **(v) -40, -20, -10, -5, -2.5, -1.25** 6. **(vi) 6, 3, 0, -3, -6, -9**

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