At the warm-up event for Oscar's All Star Hot Dog Eating Contest, Al ate one hot dog. Bob then showed him up by eating three hot dogs. Not to be outdone, Carl ate five. This continued with each contestant eating two more hot dogs than the previous contestant. How many hot dogs did Zeno (the 26th and final contestant) eat? How many hot dogs were eaten all together?

Answer:Zeno ate 51 hot dogs.

676 hot dogs were eaten all together.

Step-by-step explanation:

Al ate one hot dog. Bob then showed him up by eating three hot dogs. Not to be outdone, Carl ate five. This continued with each contestant eating two more hot dogs than the previous contestant. This means that the number of hot dogs that each contestant ate increased in an arithmetic progression.

The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1) d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 1 hot dog

d = 3 - 1 = 2 hot dogs

We want to determine the number of hot dogs eaten by the 26th contestant, T26. Therefore,

T26 = 1 + (26 - 1) 2 = 1 + 50

T26 = 51 hot dogs

The formula for determining the sum of n terms of an arithmetic sequence is expressed as

Sn = n/2[2a + (n - 1) d]

Therefore, the sum of the number of hot dogs eaten by 26 contestants, S26 would be

S26 = 26/2[2 * 1 + (26 - 1) 2]

S26 = 13[2 + 50)

S26 = 13 * 52 = 676 hot dogs