Answered

Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.


A geometric series has a sum of 1365. Each item increases by a factor of 4. If there
are 6 terms in the series, find the value of the first term.

Sagot :

edisonlara1212

Answer:

1

Step-by-step explanation:

So the sum of a finite geometric series can be defined as: [tex]S_n = \frac{a_1-a1*r^n}{1-r}[/tex] where r is the constant ratio or how much more greater the current term is, compared to the previous term (how much it's being multiplied by), and the n is the number of terms in the series. So with the given information you have the equation:

[tex]1365=\frac{a_1-a_1*4^6}{1-4}[/tex]

Simplify:

[tex]1365=\frac{a_1-4096a_1}{-3}[/tex]

Multiply both sides by -3

[tex]-4095 = a_1-4096a_1[/tex]

Subtract coefficients

[tex]-4095=-4095a_1[/tex]

Divide both sides by -4095

[tex]1 = a_1[/tex]

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.