Answer: Zeno consumed 51 hot dogs.
The total number of hot dogs consumed was 676.
Step-by-step explanation:
Al started by eating one hot dog. Bob then outperformed him by devouring three hot dogs. Carl, not wanting to fall behind, ate five hot dogs. This pattern continued, with each participant consuming two hot dogs more than the previous one. This indicates that the quantity of hot dogs eaten by each contestant followed an arithmetic sequence.
The formula for finding the nth term in an arithmetic series is given by
Tn = a + (n - 1)d
Where
a denotes the first term in the sequence.
d signifies the common difference.
n stands for the total terms in the sequence.
<pBased on the details provided,
a = 1 hot dog
d = 3 - 1 = 2 hot dogs
We aim to find how many hot dogs the 26th contestant, T26, consumed. Thus,
T26 = 1 + (26 - 1)2 = 1 + 50
T26 = 51 hot dogs
The formula to calculate the sum of n terms in an arithmetic sequence is
Sn = n/2[2a + (n - 1)d]
Hence, to find the total number of hot dogs consumed by 26 contestants, S26 is calculated as
S26 = 26/2[2 × 1 + (26 - 1)2]
S26 = 13[2 + 50]
S26 = 13 × 52 = 676 hot dogs
