*Find the sum of the first 17 terms

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In summary, the conversation discusses the concept of the sum of the first 17 terms in a sequence or series. It explains that this refers to the total value obtained by adding together the first 17 terms in a sequence or series. To find this sum, one must first identify the pattern or formula for the sequence or series and plug in the values of the first 17 terms into the formula. The conversation also clarifies the difference between a sequence and a series, with a sequence being a list of numbers that follow a specific pattern and a series being the sum of all the numbers in a sequence. The formula for finding the sum of the first 17 terms in an arithmetic sequence is n/2[2a + (n-1
  • #1
karush
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MHB
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Find the sum of the first $17$ terms of the arithmetic series:

$8+\sqrt{7}$, $6$, $4-\sqrt{7 }$...

$a_1=8+\sqrt{7}$; $n=17$; $d=2+\sqrt{7 }$

$\displaystyle\sum_{k=1}^{n}(a_1-kd)=136 \sqrt{7 }-170$

Don't have book answer for this?

Much Mahalo
 
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  • #2
Hi karush,

$$n=17,a_1=8+\sqrt7,d=-2-\sqrt7$$

Now use

$$S_n=\dfrac{n}{2}[2a_1+(n-1)d]$$
 
  • #3
$$n=17,a_1=8+\sqrt7,d=-2-\sqrt7$$
$$S_n=\frac{n}{2}[2a_1+(n-1)d]=119\sqrt{7}-136$$
 
  • #4
I got \(\displaystyle -119\sqrt{7}-136\).
 
  • #5
your right didn't see the - sign on the TI
 

FAQ: *Find the sum of the first 17 terms

What does "sum of the first 17 terms" mean?

The sum of the first 17 terms refers to the total value obtained by adding together the first 17 terms in a sequence or series.

How do you find the sum of the first 17 terms?

To find the sum of the first 17 terms, you must first identify the pattern or formula for the sequence or series. Then, plug in the values of the first 17 terms into the formula and add them together.

What is the difference between a sequence and a series?

A sequence is a list of numbers that follow a specific pattern, while a series is the sum of all the numbers in a sequence.

What is the formula for finding the sum of the first 17 terms in an arithmetic sequence?

The formula for finding the sum of the first 17 terms in an arithmetic sequence is n/2[2a + (n-1)d], where n is the number of terms, a is the first term, and d is the common difference.

Can the sum of the first 17 terms be negative?

Yes, the sum of the first 17 terms can be negative if the terms in the sequence or series are negative or if the terms cancel each other out.

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