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3 years ago

The students in Mr. T's classes wrote down the number of minutes they spent doing chores at home over a one week period:

Mathematics

1 answer:

svetoff [14.1K]3 years ago

8 0

Answer:

munanyo

Step-by-step explanation:

munanyo

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

miv72 [106K]

Hint :-

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 .

Solution :- 

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 Geometric Progression 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

7 0

2 years ago

2 of 5

34kurt

Answer: 16 of the students are girls.

Step-by-step explanation:

3/5 = boys —> 60% of students.

2/5 = girls —> 40% of students.

40% = 0.4

G = 40 * 0.4

G = 16

7 0

2 years ago

Read 2 more answers

Which shows the correct solution of the equation + so, when 6-30?

denis23 [38]

Answer:

-24

Step-by-step explanation:

rest 6 minus 30 and it give you -24

6 0

3 years ago

B) If a person is selected at random, what is the probability they have an iPhone?

quester [9]

It would be around 40 to 50% remember Apple is very popular in the United States and other countries but a lot of people prefer android phones which might be popular in their countries due to very good battery life, low cost and amazing features

7 0

3 years ago

Given g(x)=-x+2g(x)=−x+2, find g(5)g(5).

Tanya [424]

<h3>Answer: -3</h3>

Work Shown:

g(x) = -x+2

g(5) = -5+2 ... replace every x with 5

g(5) = -3

4 0

2 years ago

Read 2 more answers