Question

What is the sum of the geometric sequence 1, 4, 16, … if there are 8 terms?

21,845

43,690

65,535 (I think it is this one)

87,380

Answer 1

Okay here's the formula for a finite geometric series:
\(\huge S_n = \frac{a_1 *(1-r^n)}{1-r}\)

Now that's the formula. The key is knowing WHEN that formula is useful and WHAT the parts of it mean.
When it is useful: when you're doing a series (adding up the terms of a sequence) and the sequence is geometric, meaning the pattern is that you multiply by some number to get the next term.

What the parts of the formula mean: \(S_n\) means the sum of the first n terms. N is the number of terms. r is the "common ratio" which just means what the pattern multiplies by each time.

Answer 2

What does the a1 stand for ?

Answer 3

\(\Large a_1\) means the first term of the sequence. And in general \(\Large a_n\) means the nth term.

Answer 4

ahhhh! I see! Thank you so much!

Answer 5

You're welcome. It also wouldn't be all that bad in this case to list all 8 terms and then add them up manually. That gets to be too difficult if it's a larger list.

Answer 6

god I'm slow on replying.