Introduction: This topic is closely related to Lesson 2 (Indices). Be careful to distinguish G.P. formulas from the Arithmetic Progression (A.P.) formulas you learned in Grade 10. Questions often involve finding 'a' and 'r' first, before finding a term or a sum.

The "S Pass" Foundation (නියත S එකකට)

• Prompt 1 (Identify): Is the sequence 2, 6, 18, 54, ... a Geometric Progression? If so, what is the common ratio 'r'?

• Prompt 2 (Formula): Write down the formula for the nth term (Tn​) of a G.P.

• Prompt 3 (Calculate): Find the 6th term of the G.P. 5, 10, 20, ...

• Prompt 4 (Formula): Write down the formula for the sum of the first n terms (Sn​) of a G.P.

• Prompt 5 (Calculate): Find the sum of the first 4 terms of the G.P. 3, 6, 12, ...

Climbing to a "C" (C එකට පාර)

• Prompt 1 (Problem Solve): The 4th term of a G.P. is 54 and the common ratio is 3. Find the first term.

• Prompt 2 (Problem Solve): Which term of the G.P. 81, 27, 9, ... is equal to 271​?

• Prompt 3 (Problem Solve): The 3rd term of a G.P. is 45 and the 5th term is 405. Find the common ratio and the first term.

• Prompt 4 (Calculate): Find the sum of the first 8 terms of the G.P. 1, -2, 4, ...

• Prompt 5 (Problem Solve): How many terms of the series 3 + 6 + 12 + ... must be taken to make a sum of 381?

Aiming for a "B" (B ඉලක්කය)

• Prompt 1 (Problem Solve): The first three terms of a G.P. are (x+2), (x+12), and (x+42). Find the value of x.

• Prompt 2 (Word Problem): A person saves Rs. 10 in the first month, Rs. 20 in the second, Rs. 40 in the third, and so on. How much will they have saved in total after 8 months?

• Prompt 3 (Problem Solve): The sum of the first and second terms of a G.P. is 9, and the sum of the fourth and fifth terms is -72. Find the first 5 terms of the progression.

• Prompt 4 (Explain): Explain why there can be two possible geometric progressions if you are given the first term is 64 and the ninth term is 41​. Find the first three terms of each.

• Prompt 5 (Synthesis): The first term of a geometric progression is 'a' and the common ratio is 'r'. The sum of the first three terms is 7. The sum of the next three terms is 56. Find 'a' and 'r'.

Securing the "A" Distinction (A සාමාර්ථය තහවුරු කරගන්න)

• Prompt 1 (Challenge): The sum of the first n terms of a progression is given by the formula Sn​=4(3n−1). Show that this is a geometric progression and find its first term and common ratio.

• Prompt 2 (Word Problem): A machine depreciates in value by 20% each year. If its initial value was Rs. 500,000, what is its value after 5 years?

• Prompt 3 (Linking A.P. & G.P.): The first, third, and sixth terms of an Arithmetic Progression are the first three terms of a Geometric Progression. If the fifth term of the A.P. is 15, find the first 4 terms of the G.P.

• Prompt 4 (Sum to Infinity): A ball is dropped from a height of 20 metres. On each bounce, it rebounds to 43​ of its previous height. Find the total distance the ball travels before coming to rest.

• Prompt 5 (Proof): If a, b, and c are in a G.P., prove that loga, logb, and logc are in an A.P.