MHB *Find the sum of the first 17 terms

  • Thread starter Thread starter karush
  • Start date Start date
  • Tags Tags
    Sum Terms
AI Thread Summary
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 \(-119\sqrt{7} - 136\).
karush
Gold Member
MHB
Messages
3,240
Reaction score
5
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
 
Mathematics news on Phys.org
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
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »
Thread 'Imaginary Pythagoras'

Thread 'Imaginary Pythagoras'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Similar threads

MHB Find the sum of the first 17 terms of the arithmetic series
Replies
8
Views
3K
MHB Solve $2\cos^2(x)=1$: Find $\theta$
Replies
7
Views
2K
MHB Act.al.4 What is the 50th term
Replies
3
Views
2K
MHB Is the Sum of n^2 Terms in an Arithmetic Sequence Limited to 1?
Replies
2
Views
1K
MHB Hcc8.12 Find the sum of vectors
Replies
6
Views
2K
MHB Why is $p_i + \frac{k}{p_i}$ divisible by $3$ and $8$?
Replies
4
Views
2K
MHB Find the 79th term in the sequence
Replies
2
Views
3K
I Infinite Series of Infinite Series
Replies
7
Views
2K
MHB Challenge: Is cos(pi/60) transcendental?
Replies
1
Views
2K
MHB For which n is the term an integer & Calculate the equivalence
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top