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Geometric Sequences and Series · Paper 1 — Free Maths AI HL Practice Questions

1FoundationSAQ-SDefinition and general term of geometric sequences5 marksPaper 1~8 min

A new smartphone model is released. In its first month of sales,

5000

units are sold. The company predicts that each subsequent month, sales will be

92\%

of the sales from the previous month.

(a)

State why this situation can be modelled by a geometric sequence. [1 mark]

(b)

Find the number of units sold in the

4

th month. Give your answer to the nearest whole unit. [2 marks]

(c)

The company considers the model financially viable as long as monthly sales remain above

2000

units. Determine the month in which sales first fall below

2000

units. [2 marks]

Solutions

2MasterySAQ-SDefinition and general term of geometric sequences5 marksPaper 1~8 min

The first three terms of a geometric sequence are

x-3

x+3

, and

4x-3

, where

x \in \mathbb{R}

and

x \neq 0

(a)

Show that

x = 7

. [3 marks]

(b)

Hence find the general term

u_n

of the sequence, giving your answer in the form

u_n = a \cdot r^{n-1}

. [2 marks]

Solutions

3ChallengeSAQ-LDefinition and general term of geometric sequences8 marksPaper 1~12 min

A company is designing a logo consisting of concentric circles whose radii form a geometric sequence. The smallest circle has a radius of

2\,\text{cm}

. The radius of the fourth circle is

54\,\text{cm}

(a)

Determine the common ratio of the geometric sequence. [3 marks]

(b)

Determine the radius of the seventh circle. [2 marks]

(c)

Show that the ratio

\dfrac{A_{n+1}}{A_n}

equals

9

, where

A_n = \pi r_n^2

is the area of the

n

th circle. [1 mark]

(d)

Determine the value of

n

for which the area of the

n

th circle first exceeds

10000\,\text{cm}^2

. [2 marks]

Solutions

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