SOLUTION: Okay, so I'm having issues on how to find the nth term.. I know how to solve for the sum, which is what it wants me to do, but most of them dont give you the nth term. Please expl

Algebra ->  Sequences-and-series -> SOLUTION: Okay, so I'm having issues on how to find the nth term.. I know how to solve for the sum, which is what it wants me to do, but most of them dont give you the nth term. Please expl      Log On


   



Question 922031: Okay, so I'm having issues on how to find the nth term.. I know how to solve for the sum, which is what it wants me to do, but most of them dont give you the nth term.
Please explain what you did in each step? THANKS!!!!!
Calculate the sums of these series.
1.) +3%2F10+%2B+3%2F100+%2B+3%2F1000+%2B+3%2F10000+%2B+.+.+.+
2.) this one scared me. I dont even think i know how to solve for the sum of this +1+%2B+4%2F5+%2B+%284%2F5%29%5E2+%2B+%284%2F5%29%5E3+%2B+%284%2F5%29%5E4+%2B+.+.+.+

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
All you ask for is n-th term, means you just examine to identify the sequence pattern. Q # 2 should be obvious.

Q # 1, is almost as simple.
3/10, 3/10^2, 3/10^3, 3/10^4, .....
The exponent on the 10 is the same as the index of the term. The first term is 3%2F10%5E1.

n-th Term is 3%2F10%5En.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Okay, so I'm having issues on how to find the nth term.. I know how to solve for the sum, which is what it wants me to do, but most of them dont give you the nth term.
Please explain what you did in each step? THANKS!!!!!
Calculate the sums of these series.
1.) +3%2F10+%2B+3%2F100+%2B+3%2F1000+%2B+3%2F10000+%2B+.+.+.+
2.) this one scared me. I dont even think i know how to solve for the sum of this +1+%2B+4%2F5+%2B+%284%2F5%29%5E2+%2B+%284%2F5%29%5E3+%2B+%284%2F5%29%5E4+%2B+.+.+.+
1.
This is clearly a geometric sequence. This is seen when the 2nd term is divided by the 1st
term, and the 3rd term is divided by the 2nd term, and a common ratio (r) of 1%2F10 is obtained
%283%2F100%29%2F%283%2F10%29_____3%2F100÷3%2F10_______%283%2F100%29+%2A+%2810%2F3%29______1%2F10
%283%2F1000%29%2F%283%2F100%29____3%2F1000÷3%2F100_____%283%2F1000%29+%2A+%28100%2F3%29____1%2F10
As seen, r, or the common ratio is: 1%2F10+
a%5Bn%5D+=+a%5B1%5Dr%5E%28n-1%29, so nth term is:
highlight_green%28highlight_green%28a%5Bn%5D+=+%283%2F10%29%2A%281%2F10%29%5E%28n-1%29%29%29
2.
This is clearly a geometric sequence. This is seen when the 2nd term is divided by the 1st
term, and the 3rd term is divided by the 2nd term, and a common ratio (r) of 4%2F5 is obtained
%284%2F5%29%5E1%2F%284%2F5%29%5E0____%284%2F5%29%2F1____4%2F5÷1_____4%2F5
%284%2F5%29%5E2%2F%284%2F5%29%5E1____%2816%2F25%29%2F%284%2F5%29____16%2F25÷4%2F5_____%2816%2F25%29+%2A+%285%2F4%29, or 4%2F5
As seen, r, or the common ratio is: 4%2F5
a%5Bn%5D+=+a%5B1%5Dr%5E%28n-1%29, so nth term is:
highlight_green%28highlight_green%28a%5Bn%5D+=+%284%2F5%29%5E%28n-1%29%29%29
You need to provide the NUMBER of terms, or the value of the last term in order for the SUM of each GP to be calculated.