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M&S Learning centre 0122026649

1. The diagram shows several circles where the radii of the circles increase by 1 unit

consecutively. Show that the circumference of the circles form an A.P. Hence, find the

total circumference of the first five circles.

2. The diagram above shows three triangles with a fixed base, but their heights decrease

by 2 cm consecutively.

ashow that the area of the triangles form an A.P.b!iven that the total area of the first five triangles is 2"#cm2, find the area of the first

triangle.

c$alculate the area of all the triangles formed.

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%.

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".

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&.

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'.

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(.

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).

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1#.Two factories A and * start to +roduce gloves at the same time.

aactory A +roduced h +airs of gloves in the first month and its +roduction increases

constantly by - +airs of gloves every subseuent month. /t +roduces %## +airs of gloves

in the 0thmonth and the total +roduction for first seven months is 1'0#. ind the value of

h and -.

bactory * +roduces 2## +airs of gloves in the first month and its +roduction increases

constantly by 20 +airs of gloves every subseuent month. ind the month when both of

the factories +roduce the same total number of gloves.

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11.

$alculate

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1.!iven a geometric +rogression 2',),% find

athe common ratio

bthe 12thterm.

2.!iven a geometric +rogression ",1&,&" find

athe common ratio

bthe difference between 2ndand 0thterm.

%.The %rdterm and the 'thterm of a geometric +rogression are 1& and 20& res+ectively.

ind

a the first term and common ratio

bthe 1#thterm

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".ind the sum to infinity of the !.P "#)&,1#2",20&.

0.ind the sum of !.P 12)&, 21&..

&.A !.P has 12 terms. The first term is 3 and the last term is 1#2". ind

a the common ratio

bsum of the first 12 terms.

'.The first three terms of a !.P are x1, x41, and x40. ind

a the value of x

bthe common ratio

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(. The fourth term of a !.P exceeds the third term by & and the sum of the third and

fourth term is (. ind the first three terms of the +rogression.

).The sum of the first n terms of a !.P 1,",1&,&",.,is 21("0. ind

a the common ratio of the +rogression.

bthe value of n.

1#. !iven a !.P .. 5x+ress + in terms of .

11.5x+ress recurring decimal #.2%2%2%..as a fraction in its sim+lest form.

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12. /n a !.P, the second term is 120 and the third term is 20. $alculate

a the common ratio.

bthe sum to infinity

1%. The first three terms of a seuences are (, y,1( .inf the +ositive value of y so that the

seuence is

aan A.P

ban !.P

1".The first three terms of a !.P is ( and the sum to infinity is 2". ind

athe common ratio

bthe sum of first 0 terms

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10. The first three terms of an A.P are %1, x, y. The first three terms of a !.P are y, " and

x. $alculate the +ossible values of x and y.

1&. The sum to infinity of a !.P is and the 2ndterm is ". ind the +ossible values of

the first term.

1'. !iven 2+4, &+4 and 1"+4 are three consecutive terms of a !.P where + #.

a 5x+ress in term of +.

b ind the common ratio of the +rogression

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1(.The %rdterm and (thterms of a !.P are 2# and &"# res+ectively. ind the sum of the

first ten terms of the +rogression.

1). The common ratio of geometric +rogression is 0 and the sum of the first seven terms

is ""). ind the first term of the +rogression.

2#. /n a !.P, the first term is ( and the sum of the first three terms is 1#". ind the

+ossible values of the common ratio of the +rogression.

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21. How many terms of the geometric +rogression 0,1#,2# will give a sum of 6ust

more than 21#7

22. The sum of the first nth terms of a !.P is given as . ind

a the sum of the first three terms.

bthe "thterm

2%. 8hich term in the !.P ",12,%&,1#(,%2".. first exceed 1####7

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2".!iven the first and second terms of a !.P are ( and ". ind the sum of all the terms

after the nthterm.

20. /f log%, log) and log (1 are the first three terms of a !.P, find

a the common ratio

bthe fourth term.

2&. /n a !.P, the sum to infinity is twice the first term. 8hat is the common ratio7

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