year 8 maths

Investigation
53
6 Draw a number pyramid that has a base row of n, n + 1 and n + 2 . What is the algebraic expression
for the top number? Check this formula using some other number pyramids.
7 What is the sum of all the numbers in a pyramid with base row −10, −9, −8 ?
8 Determine an expression for the sum of all the numbers in a pyramid starting with n on the base.
Number pyramids with four consecutive numbers on the base
1 Copy and complete the following number pyramids.
60
5
17
2 4
6 8
2 Investigate how the top number is related to the starting number. Can you show this relationship using
algebra?
3 Write the sequence of all the possible top numbers less than 100 .
4 What patterns can you see in this sequence of top numbers? Can you find some way of showing these
patterns using algebraic expressions? Let the bottom row start with n . (In the examples above, n = 6
and n = 2 .)
Number pyramids with many consecutive numbers on the base
1 Determine the algebraic rule for the value of the top number for a pyramid with a base of six
consecutive numbers starting with n .
2 List the algebraic expressions for the first number of each row for several different-sized pyramids all
starting with n . What patterns can you see occurring in these expressions for:
• the coefficients of n ?
• the constants?
3 What is the top number in a pyramid with a base of 40 consecutive numbers, starting with 5 ?
4 Write an expression for the top number if the base has 1001 consecutive numbers, starting with n .
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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