8/14/2019 PSSA.20090421.ADE.arithmetic Series, Arithmetic Progression.solutions

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HOPE Charter School Tuesday, April 21, 20092009 PSSA Boot Camp

PSSA Math Reporting Categories: A Numbers and Operations

B MeasurementC Geometry

D Algebraic Concepts E Data Analysis and Probability

S O L U T I O N S Name (legibly printed): _______________________________________________

Seminar (circle one): Ackerman Beals Capers Harvey HicksonInstructions:

Place your solution into box in front of main office by end of 4 th period today. Winner will be announced during 6 th period lunch today. Winner will be randomly

selected from all entries, but the answer must be correct and justified (SHOW WORK OR EXPLAIN).

Link with questions and solutions posted at http://hopecharter.blogspot.com

The first three figures of a pattern are shown. If this pattern continues, how many dots will bein the 5 th figure?

A 11

B 13C 15

D 28

Solutions:

Solution 1: recognize a pattern, simple incrementing

The number of dots is in a sequence: 1, 3, 6

The differences between these numbers is 1 (+2) 3 (+3) 6So this is an arithmetic sequence (not a geometric sequence which involves multiplication) thatkeeps incrementing by 1.Continuing1 (+2) 3 (+3) 6 (+4) 10 (+5) 15

( N E X T P A G E )

8/14/2019 PSSA.20090421.ADE.arithmetic Series, Arithmetic Progression.solutions

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8/14/2019 PSSA.20090421.ADE.arithmetic Series, Arithmetic Progression.solutions

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So

( ) ( )

( ) ( )

( ) ( )

( ) ( )

14 4 4 1 10

21

5 5 5 1 1521

6 6 6 1 212

1200 200 200 1 201002

y x

y x

y x

y x

= = + =

= = + =

= = + =

= = + =

i

i

i

i