Question

use summation notation to write each arithmetic series for the specifies number of terms. Then evaluate the sum. 10+7+4+...; n=5

Answer 1

is that right?

Answer 2

are you sure

Answer 3

AAAaannndd the bot gets it wrong yet again!

the sum is 10+7+4+1+(-2) = 20

Answer 4

or, you can think of it as

5
∑ 13-3n = ∑13 - 3∑n = 5*13 - 3(5*6)/2 = 65 - 45 = 20
n=1

Answer 5

The arithmetic series can be written as:

$\sum_{i=1}^{5} (10-3(i-1))$

To evaluate the sum, we can simplify the expression inside the summation:

$10-3(i-1) = 10-3i+3$

$10-3(i-1) = 13-3i$

Now we can rewrite the sum using this simplified expression:

$\sum_{i=1}^{5} (13-3i)$

$= (13-3\cdot1) + (13-3\cdot2) + (13-3\cdot3) + (13-3\cdot4) + (13-3\cdot5)$

$= 13-3+13-6+13-9+13-12+13-15$

$= 60$

Therefore, the sum of the arithmetic series 10+7+4+... (with n=5) is 60.

Answer 6

Yes, that is correct.

Answer 7

Yes, I'm sure. The solution I provided uses the summation notation to write the arithmetic series and then simplifies it to evaluate the sum. The final answer is 60.

Answer 8

I apologize for the mistake in my earlier response. You are correct that the sum of the arithmetic series 10+7+4+1+(-2) (with n=5) is 20. The series can be written using summation notation as:

$\sum_{i=1}^{5} (10-3(i-1))$

Simplifying the expression inside the summation, we get:

$10-3(i-1) = 13-3i$

So the sum can be written as:

$\sum_{i=1}^{5} (13-3i)$

$= (13-3\cdot1) + (13-3\cdot2) + (13-3\cdot3) + (13-3\cdot4) + (13-3\cdot5)$

$= 13-3+13-6+13-9+13-12+13-15$

$= 20$

I hope this clears up any confusion. Thank you for bringing this to my attention.

Answer 9

Yes, that is another way to evaluate the sum of the arithmetic series. We can use the formula for the sum of an arithmetic series, which is:

$S_n = \frac{n}{2}(a_1 + a_n)$

where $n$ is the number of terms, $a_1$ is the first term, and $a_n$ is the nth term.

For the given series 10+7+4+1+(-2), we have $n=5$, $a_1=10$, and $a_n=-2$. So the formula becomes:

$S_5 = \frac{5}{2}(10 + (-2))$

$= \frac{5}{2}(8)$

$= 20$

This matches the previous result we obtained using the summation notation. Thank you for providing this alternative solution.