15Twilight
Answered

Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Given the sequence in the table below, determine the sigma notation of the sum for term 4 through term 15

Given The Sequence In The Table Below Determine The Sigma Notation Of The Sum For Term 4 Through Term 15 class=

Sagot :

naǫ
[tex]a_n=5 \ for \ n=1 \\ a_n=-10 \ for \ n=2 \\ a_n=20 \ for \ n=3[/tex]

You can see it's a geometric sequence because the ratio is constant ([tex]\frac{a_3}{a_2}=\frac{a_2}{a_1}[/tex]).
The nth term of a geometric sequence:
[tex]a_n=a_1 \times r^{n-1}[/tex]

[tex]a_1=5 \\ r=\frac{a_2}{a_1}=\frac{-10}{5}=-2 \\ \\ a_n=5(-2)^{n-1}[/tex]

It has to be the sum for term 4 through term 15, so n=4 and the number above the sigma is 15.

Your answer:
[tex]\sum^{15}_{n=4} 5(-2)^{n-1}[/tex]

Answer:

the summation of 4 times negative 3 to the n minus 1 power, from n equals 4 to 15.

Step-by-step explanation:

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.