on a tv game show,omar needs answer 7 out of every 10 questions correctly. There will be 30 questions in all

How is the series 5+11+17…+251 represented in summation notation?

NISA [10]

Answer:

$\displaystyle \large{\sum_{n=1}^{42}(6n-1)$

Step-by-step explanation:

Given:

Series 5+11+17+...+251

To find:

Summation notation of the given series

Summation Notation:

$\displaystyle \large{\sum_{k=1}^n a_k}$

Where n is the number of terms and $\displaystyle \large{a_k}$ is general term.

First, determine what kind of series it is, there are two main series that everyone should know:

Arithmetic Series

A series that has common difference.

Geometric Series

A series that has common ratio.

If you notice and keep subtracting the next term with previous term:

11-5 = 6
17-11 = 6

Two common difference, we can in fact say that the series is arithmetic one. Since we know the type of series, we have to find the number of terms.

Now that brings us to arithmetic sequence, we know that first term is 5 and last term is 251, we’ll be finding both general term and number of term using arithmetic sequence:

<u>Arithmetic Sequence</u>

$\displaystyle \large{a_n=a_1+(n-1)d}$

Where $\displaystyle \large{a_n}$ is the nth term, $\displaystyle \large{a_1}$ is the first term and $\displaystyle \large{d}$ is the common difference:

So for our general term:

$\displaystyle \large{a_n=5+(n-1)6}\\\displaystyle \large{a_n=5+6n-6}\\\displaystyle \large{a_n=6n-1}$

And for number of terms, substitute $\displaystyle \large{a_n}$ = 251 and solve for n:

$\displaystyle \large{251=6n-1}\\\displaystyle \large{252=6n}\\\displaystyle \large{n=42}$

Now we can convert the series to summation notation as given the formula above, substitute as we get:

$\displaystyle \large{\sum_{n=1}^{42}(6n-1)$

5 0

2 years ago

Ray invested $300 in Stock A

charle [14.2K]

Answer:

i think its b

Step-by-step explanation:

7 0

2 years ago

Is 1/2 between 0.1 and 0.2?

Nady [450]

No, 1/2=0.5

This is because half of one is 0.5, since 0.5 x 2 = 1.

0.1 written as a fraction would be 1/10, since 0.1 x 10 = 1.
0.2 written as a fraction would be 1/5, since 0.2 x 5 = 2

3 0

3 years ago

A bank offers a savings account that currently pays 2% interest per year compounded monthly. The amount of money in the account

LekaFEV [45]

The appropriate choice is ...
.. <span>A. The initial amount in the account does not change because it is a factor that is independent of both the interest rate and t.

_____
In general, each of the variables in a formula is independent of the others. (Occasionally, you'll see a formula where that is not true, but then the "variable" will likely be indicated as a function of those things it is dependent upon.)</span>

6 0

3 years ago

Raju bought an old car for Rs.125000 and spent Rs.25000 on its repair . He sold the car for Rs.200000 . Find his gain or loss pe

Keith_Richards [23]

Answer: $33.33\%$

Step-by-step explanation:

Given

Raju buy an old car for $Rs\ 1,25,000$

He spent $Rs\ 25000$ on its repair

The selling price of the car $Rs\ 2,00,000$

So, the cost price is

$\Rightarrow C.P.=1,25,000+25,000=Rs\ 1,50,000$

Here, $S.P.> C.P.\quad \text{i.e. gain}$

Gain percent is

$\Rightarrow \text{Gain percent}=\dfrac{2,00,000-1,50,000}{1,50,000}\times 100=\dfrac{50,000}{1,50,000}\times 100\\\Rightarrow \text{Gain percent}=33.33\ \%$

6 0

3 years ago