QUESTIONS ANSWERS

(1)

European section, season 2 Test

Arithmetic sequences

Some items of this test are multiple choice questions. They are all worth 1 point each. Other items are free response questions, all of them worth 2 points, where any incomplete or imperfect answer will be rewarded.

QUESTIONS ANSWERS

1.Ifthenumbers

16

^and

8

âreônseutive^termsⁱⁿân

arithmetisequene(inthat order),whatisthenextterm?

❒ 16

❒ 0

❒ 4

❒ − 8

2.Considerthearithmetisequene

( ¹¹ ₃ , ⁸ ₃ , ⁵ ₃ , ² ₃ , . . .)

^.^The

ommondierenein thissequeneis

❒ ¹¹

3 ❒ − 1

❒ 1

❒ − ¹ 3

3.Considerthearithmetisequenewhoseommondiereneis

5

^and^rst^term^is

8

^.^Then^the^tenth^term^is

❒ 53

❒ 58

❒ 85

❒ 77

( a n )

^suh^that

a 1 = 17

^and

a 3 = 23

^.^The^ommon^diereneⁱⁿ^this^sequene^is

❒ 6

❒ −3

❒ 3

❒ 17

(a n )

^suh^that

a 2 = 117

^and

a 12 = 187

^.^The^ommon^diereneⁱⁿ ^this^sequene^is

❒ 70

❒ − 7

❒ ⁷⁰

9 ❒ 7

6

^. ^Let

(a n )

^beânârithmeti^sequeneôf^rst^term

a 1

^and^ommon^dierene

d

^.

a

^. ^Write^any^term

a n+1

âs â^funtion ôf^the^previous^term.

b

^. ^Write^any^term

a n

âsâ^funtionôf^the^rst^termând^theômmon^dierene.

c

^. ^Let

a n

^and

a m

^be^two^termsⁱⁿ^the^sequene.^Write^down^the^relation^between^these^two^terms,

usingtheommondierene.

(2)

QUESTIONS ANSWERS

7.Thesumofthe

n

^rst^termsôfânârithmeti^sequene

(a n )

^is

givenbytheformula

❒ a 1 + a n

2 ❒ (n + 1) a 1 + a n

2 ❒ n × a 1 + a n

2 ❒ a 1 × 1 + n 2

8.Thesumofthe

5

^rst^termsôfânârithmeti ^sequeneôf^rst

term

3

^and^ommon^dierene

0.5

^is^equal^to

❒ 20

❒ 1.75

❒ 8

❒ 25 . 5

9.Consideranarithmetisequenesuhthatitsrsttermis

a 1 = − 15

^and

a 100 = 18

^.^The^sumôfîtsône^hundred^rst^terms

is

❒ 1.5

❒ 18

❒ 150

❒ − 270

10.Theommondiereneoftheprevioussequeneis

❒ ¹ ₃

❒ − ¹ 3

❒ 33

❒ 99

Pleaseanswer these lasttwoquestionson aseparate paper,withyour name onit.

11

^. ^Divide¹³⁸^hekâts ôf^barleyâmong⁸^men^so^that ^theômmon^diereneîs^3/2^hekats ôf^barley.

12

^. Â ^polygon ^has ²⁵ ^sides, ^the ^lengths ôf ^whih ^form ân ârithmeti ^sequene. Îf ^the ^polygon ^has â

perimeter of 1100m, and thelongestside is tentimes theshortestside, nd thelengthsof the

shortestandlongestsides.

QUESTIONS ANSWERS

European section, season 2 Test

Arithmetic sequences

Some items of this test are multiple choice questions. They are all worth 1 point each. Other items are free response questions, all of them worth 2 points, where any incomplete or imperfect answer will be rewarded.

QUESTIONS ANSWERS

16

8

❒ 16

❒ 0

❒ 4

❒ − 8

( 11 3 , 8 3 , 5 3 , 2 3 , . . .)

❒ 11

3

❒ − 1

❒ 1

❒ − 1 3

5

8

❒ 53

❒ 58

❒ 85

❒ 77

( a n )

a 1 = 17

a 3 = 23

❒ 6

❒ −3

❒ 3

❒ 17

(a n )

a 2 = 117

a 12 = 187

❒ 70

❒ − 7

❒ 70

9

❒ 7

6

(a n )

a 1

d

a

a n+1

b

a n

c

a n

a m

QUESTIONS ANSWERS

n

(a n )

❒ a 1 + a n

2

❒ (n + 1) a 1 + a n

2

❒ n × a 1 + a n

2

❒ a 1 × 1 + n 2

5

3

0.5

❒ 20

❒ 1.75

❒ 8

❒ 25 . 5

a 1 = − 15

a 100 = 18

❒ 1.5

❒ 18

❒ 150

❒ − 270

❒ 1 3

❒ − 1 3

❒ 33

❒ 99

11

12

( ¹¹ ₃ , ⁸ ₃ , ⁵ ₃ , ² ₃ , . . .)

❒ ¹¹

❒ − ¹ 3

❒ ⁷⁰

❒ ¹ ₃

❒ − ¹ 3