Evaluate S5 for 300 + 150 + 75 + … and select the correct answer below. 18.75 93.75 581.25 145.3125

Answers

Answer 1

Answer: It's a geometric sequence.

$300, 150, 75,... \n \n a_1=300 \n r=(a_2)/(a_1)=(150)/(300)=(1)/(2) \n \n S_n=(a_1 (1-r^n))/(1-r) \n \Downarrow \n S_5=(300(1-((1)/(2))^5))/(1-(1)/(2))=(300(1-(1)/(32)))/((1)/(2))=(300 * (31)/(32))/((1)/(2))=(75 * (31)/(8))/((1)/(2))=((2325)/(8))/((1)/(2))=(2325)/(8) * 2= \n=(2325)/(4)=581 (1)/(4)=581.25$

The answer is 581.25.

Answer 2

Answer:

we have that

$300 + 150 + 75 +...$

Let

$a1=300\n a2=150\n a3=75$

we know that

$(a2)/(a1) =(150)/(300) \n\n (a2)/(a1)=0.5 \n \n a2=a1*0.50$

$(a3)/(a2) =(75)/(150) \n\n (a3)/(a2)=0.5 \n \n a3=a2*0.50$

$a(n+1)=an*0.50$

Is a geometric sequence

Find the value of $a4$

$a(4)=a3*0.50$

$a(4)=75*0.50$

$a(4)=37.5$

Find the value of $a5$

$a(5)=a4*0.50$

$a(5)=37.5*0.50$

$a(5)=18.75$

Find $S5$

$S5=a1+a2+a3+a4+a5\n S5=300+150+75+37.5+18.75\n S5=581.25$

therefore

the answer is

$581.25$

Alternative Method

Applying the formula

$S_n=(a_1 (1-r^n))/(1-r) \n\na_1=300 \n r=(1)/(2)\n\n S_5=(300(1-((1)/(2))^5))/(1-(1)/(2))\n\n=(300(1-(1)/(32)))/((1)/(2))\n\n=(300 * (31)/(32))/((1)/(2))\n\n=(75 * (31)/(8))/((1)/(2))\n\n=((2325)/(8))/((1)/(2))\n\n=(2325)/(8) * 2\n\n=(2325)/(4)\n\n=581 (1)/(4)\n\n=581.25$

therefore

the answer is

$581.25$

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Answers

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