Ask your own question, for FREE!
Mathematics 23 Online
OpenStudy (anonymous):

Find the sum of the series or state that the sum does not exist. 5 + 7.5 + 11.25 + ... and 16 + 12 + 9 + ...

OpenStudy (anonymous):

the 16+12+9 doesn't exist right?

jimthompson5910 (jim_thompson5910):

Do you know what kind of sequence you're dealing with here?

OpenStudy (anonymous):

geometric right?

jimthompson5910 (jim_thompson5910):

you are correct

jimthompson5910 (jim_thompson5910):

Notice how 7.5/5 = 1.5 and 11.25/7.5 = 1.5, so this shows us that we're multiplying each term by 1.5 to get the next term

OpenStudy (anonymous):

yes i see that

jimthompson5910 (jim_thompson5910):

Now do you know the rule for summing terms in an geometric sequence? Specifically the rule of summing an infinite number of terms.

OpenStudy (anonymous):

r<1?

jimthompson5910 (jim_thompson5910):

Close, it's more like |r| < 1 If that is true, then the infinite sum exists.

OpenStudy (anonymous):

so this sum does not exist

jimthompson5910 (jim_thompson5910):

So in the case of r = 1.5, |r| < 1 is false since |1.5| < 1 is false

OpenStudy (anonymous):

but the other one is 64 right?

jimthompson5910 (jim_thompson5910):

So you are correct, the infinite sum doesn't exist for the first sequence.

jimthompson5910 (jim_thompson5910):

The first term is 16. So a = 16 What is the value of r in the second sequence?

OpenStudy (anonymous):

.75

jimthompson5910 (jim_thompson5910):

Good, so the infinite sum is S = a/(1-r) S = 16/(1-0.75) S = 64 So you are correct.

OpenStudy (anonymous):

thanks!

jimthompson5910 (jim_thompson5910):

you're welcome

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!