Weekly Math Problem #82

Geometric Series. This week's problem is a second part to last week's problem, WMP #81. Since we looked at a geometric sequence last week, why don't we look the corresponding geometric series this week? Well...we are. ✏️ 👍🏿

To solve this week's problem in completion, you need to recall the following math skills and information:

       ✔️     How to find the sum of the first set of numbers from a geometric sequence  

            

WMP #82 says to...

Happy solving!

Check back on Saturday, April 30th for the solution, which will be posted below ⬇️.

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✏️📓 Solution Time! 📓✏️

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And we're back! Of course, to find the sum of the first eight terms of our (or any) geometric series, we can write it down and find the sum manually...but...what if, instead of eight terms, we had had to find eighteen terms?! I don't want to write that many terms. And guess, what? We don't have to. There's a formula for that!

Here is the formula:

In our situation, we have the following:

Well, it looks like the sum of the first eight terms of the geometric series whose first term is 2 with a ratio of 3 is 6560.

Now, just for fun, let's find the sum manually to verify that we've used the formula correctly. (This will also help us to appreciate the formula more.) Here are the first eight numbers generated from last week's geometric sequence with its corresponding sum:

...And it's a match! 

▪️ Did you find this problem easy? Hard? Somewhere between easy and hard?

▪️ Leave a comment to let me know what you thought about this week's problem. 

Thank you for solving with me this week. ✏️
WMP! #83 is up next. 🤓

Cheers!

The Younge Lady