A man 12

A man in his will shared his money geometrically among his six sons, so the eldest son received #5,589 and the youngest son received #736.

(A)How much will the fourth son receive?
(B)How much was shared among them

Correct answer:

g₄ =  2484
s =  15295

Step-by-step explanation:

$$\begin{gathered} g_6=5589 \\ {g}_1=736 \\ {g}_6=q_1\cdot q^5 \\ q=\sqrt[5]{g_6/g_1}=\sqrt[5]{5589/736}=\frac{3}{2}=1\frac{1}{2}=1.5 \\ {g}_4=g_1\cdot q^3=736\cdot 1.5^3=2484 \end{gathered}$$

$$\begin{gathered} g_5=g_4\cdot q=2484\cdot 1.5=3726 \\ {g}_3=g_4/q=2484/1.5=1656 \\ {g}_2=g_3/q=1656/1.5=1104 \\ {g}_1=g_2/q=1104/1.5=736 \\ s=g_1+g_2+g_3+g_4+g_5+g_6=736+1104+1656+2484+3726+5589=15295 \end{gathered}$$

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