SOLUTION: evaluate the series to the given term 1. 256 + 192 + 144 + ...; S7 2. 1 – 3 + 9 – 27 + ...; S10 3. –14 + (–7) + 0 + 7 + ...; S10

Algebra ->  Sequences-and-series -> SOLUTION: evaluate the series to the given term 1. 256 + 192 + 144 + ...; S7 2. 1 – 3 + 9 – 27 + ...; S10 3. –14 + (–7) + 0 + 7 + ...; S10      Log On


   

Question 453276: evaluate the series to the given term
1. 256 + 192 + 144 + ...; S7
2. 1 – 3 + 9 – 27 + ...; S10
3. –14 + (–7) + 0 + 7 + ...; S10
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
the sum of the first n terms of a geometric series is given by the formula
S%5Bn%5D+=+a%5B1%5D%2A%28%281-r%5En%29%2F%281-r%29%29,
where a%5B1%5D = the first term of the series, and r = common ratio.
1. a%5B1%5D+=+256, r = 3/4.
==>
2. a%5B1%5D+=+1, r = -3.
S%5B10%5D+=+1%2A%28%281-%28-3%29%5E10%29%2F%281-%28-3%29%29%29+=+-14762

3. This is an arithmetic series, so S%5Bn%5D+=+a%5B1%5D+%2B+%28n-1%29d+=+-14+%2B+9%2A7+=+-14+%2B+63+=+49.