Question

Q: Imagine that there are 30 students in a magical room and the first student got an egg from the master but due to the magical effects of that room, the second student got double the amount the first student had. Then he gave all the eggs to his friend beside him and continued till the 30th student. Calculate the number of eggs the 30th student has in the first case. And if the first person had given only one egg to his partner and partner's partner and so on and on and on till 30th student. Calculate the number of eggs the 30th student had in the second case



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Answer 1

Answer:

$\huge\red{ \boxed{ answer \implies \: 536870912}} \\ \\ first \: person \: has \: one \: egg \\ so \: then \: second \: one \: got \: 2 \\ \\ first \: person \: have \: egg \implies \: 1 \\ \\ second \: have \implies \: 2 \\ \\ so \: first \: term \: is \: 1 \: (a = 1) \: \\ \\ \: and \: common \: ratio \: of \: this \: series \\ is \: 2 \: (r = 2) \\ \\ this \: series \: is \: an \: gp \\ so \\ \: n \: th \: term \: of \: this \: geometric \: sequence \: \\ is \\ \\ an = a \: {r}^{n - 1} \\ \\ so \\ \\ a30 = 1 \times {2}^{30 - 1} \\ \\ \implies \: {2}^{29} \\ \\ \implies \: 536870912 \\ \\ so \: 30th \: person \: got \:536870912eggs$

Answer 2

Step-by-step explanation:

$\sf\pink{first \: person \: has \: 1egg} \\ \sf\pink{second \: have \: = 2 } \\ \sf\pink{here \: a = 1 \: \: a2 = 2} \\ \sf\pink{r = 2} \\ \sf\pink{an = {ar}^{n - 1} } \\ \sf\pink{a30 = 1 \times {2}^{30 - 1} } \\ \sf\pink{ = > {2}^{29} } \\ \sf\pink {\underline{hope \: it \: help \: you} }$