Geometric Progressions

Welcome to class!

In today’s class, we will be talking about geometric progressions. Enjoy the class!

The sequence 5, 10, 20, 40 has a first term of 5 and the common ratio

Between the term is 2 e.g. (¹⁰/₅ or ⁴⁰/_2o = 2).

A sequence in which the terms either increase or decrease in a common ratio is called a Geometric Progression

(G. P)

Denotations in G. P

a = 1^st term

r = common ratio

U_n = nth term

S_n = sum

The nth term = Un

Un = ar^n-1

1^st term = a

2^nd term = a x r =ar

3^rd term = a x r x r = ar²

4^th term = a x r x r x r = ar³

8^thterm = a x r x r x r x r x r x r x r = ar⁷

nth term = a x r x r x r x ……….. ar^n-1

In the 2^nd and 4^th term of a G.P are 8 and 32 respectively, what is the sum of the first four terms. (a) 28 (b) 40 (c) 48 (d) 60
The sum of the first five terms of the G.P. 2, 6, 18, is (a) 484 (b) 243 (c) 242 (d) 130
The 4^th term of a GP is -2/3 and its first term is 18 what is its common ratio. (a) ½ (b) ¹/₃(c) ^-1/₃ (d) ^-1/₂
If the 2^nd and 5^th term of a G. P. are -6 and 48 respectively, find the sum of the first four terms: (a) -45 (b) -15 (c) 15 (d) 33
Find the first term of the G.P. if its common ratio and sum to infinity – ³/₃ and respectively (a) 48 (b) 18 (c) 40 (d) -42

In our next class, we will be talking about the Quadratic Equation. We hope you enjoyed the class.

Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.