Question

Look at this pattern


1^2+(4 × 2) =3^2



2^2+(4 × 3) =4^2


3^2+(4 × 4) =5
^2

i) Write the next two lines. (1)

ii) Explain the general principle using algebra.​

Answer 1

Answer:

ANSWERS TO EXERCISES

EXERCISE 1

a n − 3 bananas in each crate b 7(n − 3) bananas in total

EXERCISE 2

a 20(s + 5) seats in total

EXERCISE 3

a 270 b 27 000

EXERCISE 4

a b + 2 b a + 3, a + 6 c n − 2

EXERCISE 5

x C8g12.pdf 2x − 5 C8g13.pdf 3(2x − 5) = 6x − 15 C8g14.pdf 6x 6x − 5x = x

EXERCISE 6

Sum of the first n odd numbers is: 1 + 3 + 5 + …. + (2n − 5) + (2n − 3) + (2n − 1)

Reverse the sum: (2n − 1) + (2n − 3) + (2n − 5) + … + 5 + 3 + 1

Add to the original sum pairing terms yields

(2n − 1 + 1) + (2n − 3 + 3) + … + (3 + 2n − 3) + (1 + 2n − 1) = 2n × n =2n2

The sum is n2

EXERCISE 7

a n + 1000 tonnes b tonnes

EXERCISE 8

a 7x + 4 b 14x + 38 c 8x + 11

Step-by-step explanation:

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