what is the sum of the geometric sequence -4, 24, -144... if there are 7 terms?

Question

primeralph · Answer

@Jhannybean  Please do this.

ivettef365 · Answer

those are multiple of -6

jhannybean · Answer

formula for finding the sum of a geometric sequence is $$\large a\left ( \frac{1-r^{n}}{1-r} \right )$$$$\large {n= 7 \r = -6\ a = -4 }$$ your "a" is the first term present, your ratio is found by dividing the preceding term by previous term, and  your "n" is the number of terms you want to find in your sequence. 
$$r = \frac{24}{-4} = -6 \ , \ \frac{-144}{24} =  -6 \, \ ...$$plugging these values in. $$\large -4 \left ( \frac{1-(-6)^{7}}{1-(-6)}\right )$$$$\large -4 \left ( \frac{279937}{7} \right )=-159964$$

anonymous · Answer

thank you very much!

jhannybean · Answer

Do you understand how it is found? it is a lot different than finding sums of geometric series.

jhannybean · Answer

Not sure if you've learned those yet...