Nalanda College, Colombo 10 Grade 11 Maths Worksheet: 16 Geometric Progression

First term from ratio and a later term

Answer: 4

💡 What it's asking: In a geometric progression (GP) each term is the one before multiplied by the same number r, the common ratio. Use the nth-term rule Tn = ar^(n−1) to work back to the first term a.

1. 1Write the rule for the 6th term: T6 = a × r^5, because you multiply by r five times to get from T1 to T6.
2. 2Put r = 2: 2^5 = 32, so T6 = 32a.
3. 3The 6th term is 128, so 32a = 128.
4. 4Divide both sides by 32: a = 128 ÷ 32 = 4.

✅ Start at 4 and keep doubling: 4, 8, 16, 32, 64, 128. The 6th term is 128, so it works.

Which term equals a given value

Answer: 8th term

💡 What it's asking: We want the position n of the term −256. Write the nth term with the rule Tn = ar^(n−1), set it equal to −256 and solve for n by matching powers of 2.

1. 1Here a = −2 and r = 2, so Tn = −2 × 2^(n−1).
2. 2Set it equal to the target: −2 × 2^(n−1) = −256.
3. 3Divide both sides by −2: 2^(n−1) = 128.
4. 4Write 128 as a power of 2: 128 = 2^7, so n − 1 = 7.
5. 5Add 1: n = 8, so −256 is the 8th term.

✅ List the terms: −2, −4, −8, −16, −32, −64, −128, −256. The 8th one is −256.