Question

A gardener wanted to reward a girl for her good deeds by giving some apples. He gave 2 apples on the first day, 4 on the second day, 8 on the third day, 16 apples on the fourth day and so on for ten days. How many apples did she get from the gardener at the end of the tenth day

Answer 1

2^10 = 1024 apples at the end of tenth day

Answer 2

Given,

/* A gardener wanted to reward a girl for her good deeds by giving some apples. He gave 2 apples on the first day, 4 on the second day, 8 on the third day, 16 apples on the fourth day and so on for ten days.*/

$Day \:wise \: apples \:the \: received : \\2,4,8,16,\cdot \cdot \cdot ,10\:days$

$Here , First \:term (a) = 2$

$\frac{a_{2}}{a_{1}} = \frac{4}{2} = 2$

$\frac{a_{3}}{a_{2}} = \frac{16}{8} = 2$

$\implies \frac{a_{2}}{a_{1}} = \frac{a_{3}}{a_{2}} = 2$

$Given \: sequence \:is \: G.P .$

$Common \:ratio (r) = 2$

$\boxed{\pink { Sum \:of \:n\:terms (S_{n}) = \frac{a(r^{n}-1)}{r-1}}}$

$Sum \:of \:10 \:terms (S_{10}) = \frac{2(2^{10}- 1)}{2-1} \\= \frac{2(1024-1)}{1} = 2\times 1023 \\= 2046$

Therefore.,

$\green { She \:get \:2046 \: apples \:at \:the }\\\green {end \:of \:the \:tenth \:day }$

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