Answer to Question #210558 in Algebra for Sfiso Mngomezulu

Question

Generalise your findings to

predict what you will observe

in the sum of

(a) five consecutive multiples

of 10 like (30 + 40 + 50 +

60 + 70)

(b) three consecutive

numbers like

(7 + 8 + 9)

(c) seven consecutive

numbers like

(2 + 3 + 4 + 5 + 6 + 7

+ 8)

Answer 1

(a) five consecutive multiples

of 10 like

$30 + 40 + 50 + 60 + 70=250\\250\div5=50$

The middle number is 50

therefore $50\times 5=250$

The sum of any consecutive five numbers

equals the fifth multiple of the middle

number or equals the product of five and

the middle number.

(b) three consecutive

numbers like

$7 + 8 + 9=24\\24\div3=8$

The middle number is 8

therefore $8\times 3=24$

The sum of any consecutive three numbers

equals the third multiple of the middle

number or equals the product of the three and

the middle number.

(c) seven consecutive

numbers like

$2 + 3 + 4 + 5 + 6 + 7 + 8=35\\24\div7=5$

The middle number is 5

therefore $5\times 7=35$

The sum of any consecutive seven numbers

equals the fourth multiple of the middle

number or equals the product of the seven and

the middle number.