Progression

Question 1

How do you determine the nth term of an Arithmetic Progression (A.P.)?

Answer 1

1. Identify the First Term (a): The first term of the sequence.

2.Identify the Common Difference (d): The difference between consecutive terms.

3. Use the Formula: 𝑇ₙ = 𝑎 + (𝑛 − 1) 𝑑 Tₙ where 𝑇ₙ is the nth term, 𝑎 is the first term, and 𝑑 is the common difference.

Question 2

How do you determine the nth term of a Geometric Progression (G.P.)?

Answer 2

1. Identify the First Term (a): The first term of the sequence.
2. Identify the Common Ratio (r): The ratio between consecutive terms.
3. **Use the Formula: 𝑇ₙ = 𝑎𝑟(ⁿ⁻¹) where
   𝑇ₙ is the nth term, 𝑎 is the first term, and
   𝑟 is the common ratio.

Question 3

How do you compute the sum of the first n terms of an Arithmetic Progression (A.P.)?

Answer 3

1. Use the Formula: 𝑆ₙ = 𝑛 / 2 [2𝑎 + (𝑛 −1)𝑑] where 𝑆ₙ is the sum of the first n terms, 𝑎 is the first term,
   𝑑 is the common difference, and
   𝑛 is the number of terms.
2. Alternate Formula: 𝑆ₙ = 𝑛 / 2 (𝑎 + 𝑙) where 𝑙 is the last term.

Question 4

How do you compute the sum of the first n terms of a Geometric Progression (G.P.)?

Answer 4

1. Use the Formula: 𝑆ₙ = 𝑎 ( (1−𝑟ⁿ) / (1 − 𝑟) ) for 𝑟 ≠ 1, where 𝑆ₙ is the sum, 𝑎 is the first term, 𝑟 is the common ratio, and
   𝑛 is the number of terms.
2. If 𝑟 = 1: The sum is 𝑆ₙ = 𝑎𝑛.

Question 5

How do you compute the sum to infinity of a Geometric Progression (G.P.)?

Answer 5

1. Condition: This only applies if the common ratio ∣𝑟∣ < 1.
2. Use the Formula: 𝑆∞ = 𝑎 / (1−𝑟) where 𝑆∞
   is the sum to infinity, 𝑎 is the first term, and 𝑟 is the common ratio.