Raymond was raising the chickens on the farm. The first week,2chicks hatched. the second week, 7 chicks hatched. The 3erd week, 17 chicks hatched. 317 chicks where hatched on the seventh week

Question

1.If the pattern continued, how many chicks hatched in the 4,5,6 weeks?

2.What is the pattern?

Answer 1

The pattern is shown here:

Wk 1 2 chicks

Wk 2 7 chicks (2+5)

Wk 3 17 chicks (2+5+10)

Wk 4 37 chicks (2+5+10+20)

Wk 5 77 chicks (2+5+10+20+40)

Wk 6 157 chicks

Wk 7 317 chicks

...

Wk n 2+5+10+20+...=2+5(1+2+2²,+...+2^(n-2))=2+5(2^(n-1)-1).

In simple terms, each week sees double the chicks added compared to the week before.