2.What is the sum of the geometric sequence 4, 12, 36 … if there are 9 terms? (1 point)

Question

anonymous · Answer

well do you know what the sequence is?

hartnn · Answer

and can you find out the common ratio (r) first ??

anonymous · Answer

because if you look 4*3 =12
12*3=36 so the sequence must be x*3=y
so your sequence chain would be 4, 12, 36, 108, 324, 972, 2916, 8748, 26244.
4+12+36+108+324+972+2916+8748+26244= 39364
This is the answer as well as the steps to get said answer

hartnn · Answer

or you could use the formula for the sum of terms of a geometric sequence.
This formula especially is useful when you have many terms
$\Large S_n = a_1 \dfrac{r^{n}-1}{r-1}$

hartnn · Answer

a1 = first term = 4 here
r= common ratio =...?
n = number of terms = 9 here

anonymous · Answer

thanks @hartnn  i had completely forgotten about that formula.

hartnn · Answer

oh, you're welcome ^_^

anonymous · Answer

:)

anonymous · Answer

so it would be
$$4(\frac{ 3^9-1 }{ 3-1 })$$ = 39364

anonymous · Answer

thats a lot easier then the method i used