addmaths form 5 gp examples

7/24/2019 Addmaths Form 5 GP Examples

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Chapter 1: Progression 1.2 :Geometric Progression Name:Jan 18, 2016

EXAMPLES

1n

n arT

=the nth term of a geometric progression (G.P.):

the common ratio is related to the formula: 1n

n

2

3

1

2

T

T......

T

T

T

Tr

==

the sum of the first nth terms of a geometric progression:

r

raS

n

n

=

1

)(1

1

1

=r

raS

n

n

, r 1 , r 1

the sum to infinity of G.P. :

1. State the common ratio, r, and the 8thterm of the geometric progression,......004.0,0004.0,00004.0

. !etermine the si"th term and the fifteenth tern of each of the follo#ing geometric progression.

(a) ,......$4,18,%,

(&) ,......4,48,'%

. he nth term of a geometric progression is gi*en &y

n

nT

1

=

. +ind

(a) the first term,

(&) the common ratio.

4. alculate the num&er of terms in each of the follo#ing geometric progressions.

(a) 48%

1,.......,

18

1,

%

1,

1

.

(&) %4

((10,.......,

11(,',%

.

$. Gi*en that %,(, +++ yyy are the first three terms of a geometric progression, find(a) the *alue ofy,

(&) the 'thterm of the progression.

%. Gi*en a geometric progression,,......,

1%,4, nm

m , e"press nin terms of m.

1

r

a

S

1


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-. Gi*en that 108, a, b, cand %4

-

are the first fi*e terms in a G.P., find the *alues of a,band c.

8. +or the geometric progression -$0, 1$0, 0,.., #hich term #ill &e less than $

1

for the first time/

'. he third term and the se*enth term of a geometric progression are 1 and 1' respecti*ely. +ind 'T

.

10. n a geometric progression, the first term is aand the common ratio is r. f the third term e"ceeds the

second term &y 0a, find the *alues of r.

11. +ind the sum of the first - terms of each of the follo#ing geometric progressions.

(a) %, %0, %00,.

(&) 40'%, 104, $%,.

1. Gi*en a geometric progression,.....$,1,

$

1

, find the sum of the fourth term to the eight term.

1. he sum of a geometric progression,......10,,

$

, is $

1$%

. +ind the num&er of terms in the

geometric progression.

14. +or the geometric progression , 10. $0,., calculate the least num&er of terms that must &e taen for

the sum to e"ceed 1$00.

1$. n year 00-, 2ohan deposited 3$000 into his &an account. 5e earns an interest of $6 per annum of

the amount standing in the account at the time. +ind

(a) the amount of money in the account in year 011,

(&) the year in #hich there #ill &e more than 38000 for the first time in the account.

1%. +ind the sum to infinity of the geometric progression $%0, 140, $,.

1-. he third term and the fifth term of a geometric progression are $

1

and 1$

1

respecti*ely. Gi*en that all

the terms are positi*e, find the sum to infinity.

18. 7 geometric progression is such that the sum of the first three terms is 14 and the sum to infinity is 1%.

+ind the first term of the progression.

1'. "press each of the follo#ing decimals as a fraction or mi"ed num&er.

(a) 0.4$4$4$4..

(&) 1.%%%..

(c)

$.0

(d)

%(0.0

0. he diagram sho#s the arrangement of the first three circles of an infinite series of similar circles. he

first circles has a radius of rcm. he radius of each su&se9uent circle is half of its pre*ious one.

cmr


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(a) Sho# that the areas of the circles form a geometric progression and state the common ratio.

(&) Gi*en that the diameter of the first circle is 40 cm.

(i) determine #hich circle has an area of

cm

$%

$

,

(ii) find the sum to infinity of the areas, in cm, in terms of .

addmaths form 5 gp examples

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