MHB *Find the sum of the first 17 terms

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The discussion focuses on finding the sum of the first 17 terms of an arithmetic series starting with \(8+\sqrt{7}\) and having a common difference of \(d = -2 - \sqrt{7}\). The initial term is \(a_1 = 8+\sqrt{7}\) and the formula for the sum of the first \(n\) terms is applied. One participant calculates the sum as \(S_n = 119\sqrt{7} - 136\), while another corrects it to \(-119\sqrt{7} - 136\) after noticing a sign error. The conversation highlights the importance of careful calculation and attention to signs in arithmetic series problems. The final result is confirmed as \(-119\sqrt{7} - 136\).
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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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Hi karush,

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

Now use

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