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photoshop1234 [79]

2 years ago

11

Answer please please please please

2 answers:

zhannawk [14.2K]2 years ago

5 0

Answer: 3.25

Step-by-step explanation:

Viefleur [7K]2 years ago

4 0

Answer:

3.25

Step-by-step explanation

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Given the sequence 1/2 ; 4 ; 1/4 ; 7 ; 1/8 ; 10;.. calculate the sum of 50 terms

miv72 [106K]

<u>Hint </u><u>:</u><u>-</u>

Break the given sequence into two parts .
Notice the terms at gap of one term beginning from the first term .They are like $\dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8}$ . Next term is obtained by multiplying half to the previous term .
Notice the terms beginning from 2nd term , $4,7,10,13$ . Next term is obtained by adding 3 to the previous term .

<u>Solution</u><u> </u><u>:</u><u>-</u><u> </u>

We need to find out the sum of 50 terms of the given sequence . After splitting the given sequence ,

$\implies S_1 = \dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8}$ .

We can see that this is in <u>Geometric</u><u> </u><u>Progression </u> where 1/2 is the common ratio . Calculating the sum of 25 terms , we have ,

$\implies S_1 = a\dfrac{1-r^n}{1-r} \\\\\implies S_1 = \dfrac{1}{2}\left[ \dfrac{1-\bigg(\dfrac{1}{2}\bigg)^{25}}{1-\dfrac{1}{2}}\right]$

Notice the term $\dfrac{1}{2^{25}}$ will be too small , so we can neglect it and take its approximation as 0 .

$\implies S_1\approx \cancel{ \dfrac{1}{2} } \left[ \dfrac{1-0}{\cancel{\dfrac{1}{2} }}\right]$

$\\\implies \boxed{ S_1 \approx 1 }$

$\rule{200}2$

Now the second sequence is in Arithmetic Progression , with common difference = 3 .

$\implies S_2=\dfrac{n}{2}[2a + (n-1)d]$

Substitute ,

$\implies S_2=\dfrac{25}{2}[2(4) + (25-1)3] =\boxed{ 908}$

Hence sum = 908 + 1 = 909

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2 years ago

patty is building a rope ladder for a tree house. she needs two 5-foot pieces of rope for th esides fo the ladder. she needs 7 p

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2 years ago

Please show your work, Due at 11:30. Please help!!!

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Answer:

1. 3217

x 56

_____________

19302

160850

__________

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x 27

_________

39830

113800

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3. 213

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Step-by-step explanation:

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3 years ago

At the store, Sam bought 4 hats for $65. What is the cost of 1 hat?

kupik [55]

Answer:

$16.25

Step-by-step explanation:

4 hats cost $65

1 hat cost 65/4=16,25

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2 years ago

Diana's parents keep a chart on the wall where they mark how much Diana grows each year. When Diana was 15, she grew 5/6 of an i

otez555 [7]

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2 years ago

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