MHB *Find the sum of the first 17 terms

[karush]

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

 

[Greg]

Hi karush,

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

Now use

$$S_n=\dfrac{n}{2}[2a_1+(n-1)d]$$

 

[karush]

$$n=17,a_1=8+\sqrt7,d=-2-\sqrt7$$
$$S_n=\frac{n}{2}[2a_1+(n-1)d]=119\sqrt{7}-136$$

 

[suluclac]

I got $$-119\sqrt{7}-136$$.

 

[karush]

your right didn't see the - sign on the TI