Sequences and Series, I am struggling and need help.

[neb2]

I could really use some help with sequences and series. I don't understand how the equations are suppose to work. I seem to be struggling with the problems.

State the first five terms of the sequence if a1=4 and an+1=-3an

Find the 10th term of the sequence 5, 15, 45,.....

Find the sum of each infinate geometric series.
5+6+7.2+... _________
E3(1/2)n-1 ___________

Find the Recursive and explicit (nth term) formulas for the sequence.
81, -54, 36, -24 Recursive: ____________Explicit: ____________

Find 2 geometric means between 6 and 60.25.
________,__________
Find 3 arithmetic means between -25 and 5
________,__________,_________

Thanks in advance for the help.

 

[skeeter]

I could really use some help with sequences and series. I don't understand how the equations are suppose to work. I seem to be struggling with the problems.

State the first five terms of the sequence if a1=4 and an+1=-3an

each term is -3 times the previous term ...
4, -12, 36, -108, ...

Find the 65th term of the sequence 9, 15, 21, 27,.....

an arithmetic sequence ... see the common difference of 6?

a_n = a₁ + (n-1)d where d is the common difference

so ... a₆₅ = 9 + (64)6 = 393


Find the sum of each infinate geometric series.

sum of an infinite geometric series is a₁/(1 - r), where r is the common ratio. find r by dividing any term by the term immediately before it .

-15+5+5/3+... _________ did you mean 15 + 5 + (5/3) + ... ?
what's up with the negative sign infront of the 15?

E-4(3/4)n-1 ___________ what is this?

Find the Recursive and explicit (nth term) formulas for the sequence.
-3, 4, 11, 18 Recursive: ____________Explicit: ____________

recursive ... a_n+1 = a_n + 7
explicit ... a_n = -3 + (n-1)7

Find 2 geometric means between 6 and 60.25.
________,__________ geometric mean of a and b = sqrt(ab)

Find 3 arithmetic means between -25 and 5 arithmetic mean of a and b = (a+b)/2
________,__________,_________

Thanks in advance for the help.

 

[neb2]

E-4(3/4)_n-1 ___________ what is this?

[E = Summation Symbol] -4 (3/4)n-1 [n-1 sub notation]
I got the answer of 16, not sure how right it is.

what's up with the negative sign infront of the 15?

I think the equation in my review packet has a typo. I got an answer of 45/2 ignoring the negative.

Find the sum of each infinate geometric series.
5+6+7.2+... _________
E3(1/2)n-1 ___________