Answer :
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