Question

Lerna’s Hydra is a mythological character that appears in some stories such as the 12 Tasks of Hercules. The Hydra was a one-headed monster but when it is cut off, 2 more heads grow in its place. If a hero tried to conquer it by cutting off all of its heads every day, how many heads would the Hydra have on the 10th day?

Answer 1

Answer:

512

Step-by-step explanation:

Assuming Hydra's head grows out next day only.

We start with 1 head, it turns 2 next day and keeps on doubling every day.

It will be a geometric progression with common ration (r) = 2 and initial term (a) = 1.

we know,

  n-term = ar^(n-1)

So, on 10th day

Number of head = 2^9  = 512

Answer 2

Hydra would have 512 heads on the tenth day.

Explanation:

Given Hydra's head grows when it is cut we can assume that new heads grow the next day only. So, we start with one head the first day then two more on the next day, and so on.

If you notice closely, it will be a geometric progression with a common ratio of 2 and initial term 1.

According to the formula,

a(n) = a ($r^{n-1}$), where,

a= initial term

r= common ratio

a(n)= nth term  

∴ On the 10th day  

Number of heads = 1($2^{10-1}$)

                              = $2^{9}$ = 512