Question

b) A father distributed some amount to his four sons in GP His elderson gon R 1000
and his younger son got Rs 512 then how much amount the father distributed to
his sons​

Answer 1

Answer:

2 elder = R 2000

2 younger = R 1024

total = R 3024

Answer 2

The amount distributed by father  among his sons=Rs 2952

Step-by-step explanation:

Let four terms of G.P are

$a,ar,ar^2,ar^3$

According to question

$a=512$

$ar^3=1000$

Substitute the value of a

$512r^3=1000$

$r^3=\frac{1000}{512}$

$r^3=(\frac{10}{8})^3$

When power equal on both sides of equality then, the base will be equal therefore,

$r=\frac{10}{8}=\frac{5}{4}$

n=4

Sum of nth terms in G.P is given by

$S_n=\frac{a(r^n-1)}{r-1}$ Where r>1

Using the formula

$S_4=\frac{512((\frac{5}{4})^4-1)}{\frac{5}{4}-1}$

$S_4=\frac{512\times (\frac{625}{256}-1}{\frac{5-4}{4}}$

$S_4=\frac{512\times(\frac{625-256}{256})}{\frac{1}{4}}$

$S_4=\frac{512\times 369\times 4}{256}=2952$

Hence, the amount distributed by father  among his sons=Rs 2952

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