Back to: MATHEMATICS SS2

**Welcome to class! **

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

**Geometric Progressions**

**Definition of G.P**

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)

- P: a, ar, ar
^{2}, ar^{3}………………

Denotations in G. P

a = 1^{st} term

r = common ratio

U_{n} = nth term

S_{n} = sum

**The nth term of a G. P**

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 = ar^{2}

4^{th} term = a x r x r x r = ar^{3}

8^{th}term = a x r x r x r x r x r x r x r = ar^{7}

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

**General Evaluation**

- 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.

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