SOLUTION: 2. Consider the geometric sequence 8, 12, 18, 27, … (a) Find the formula for its general term. (b) Find its 17th term to 3 significant figures. (c) Use algebra to find out

Algebra ->  Sequences-and-series -> SOLUTION: 2. Consider the geometric sequence 8, 12, 18, 27, … (a) Find the formula for its general term. (b) Find its 17th term to 3 significant figures. (c) Use algebra to find out       Log On


   

Question 991841: 2. Consider the geometric sequence 8, 12, 18, 27, …
(a) Find the formula for its general term.
(b) Find its 17th term to 3 significant figures.
(c) Use algebra to find out which is the least term of the sequence greater than 1000
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
8, 12, 18, 27
(a) Find the formula for its general term.
We find the common ratio by dividing each term after the
first by the preceding term

12%2F8=3%2F2, 18%2F12=3%2F2, 27%2F18=3%2F2 

So r=3%2F2=1.5

Use standard formula

a%5Bn%5D=a%5B1%5Dr%5E%28n-1%29+

a%5Bn%5D=8%281.5%29%5E%28n-1%29

(b) Find its 17th term to 3 significant
figures.
Substitute 17 for n

a%5B17%5D=8%281.5%29%5E%2817-1%29

a%5B17%5D=5254.727

(c) Use algebra to find out which is the
least term of the sequence greater than 1000.
a%5Bn%5D=8%281.5%29%5E%28n-1%29%3E1000

log%28%288%281.5%29%5E%28n-1%29%29%29%3Elog%28%281000%29%29

log%28%288%29%29%2Blog%28%281.5%29%5E%28n-1%29%29%3E3

log%28%281.5%29%5E%28n-1%29%29%3E3-log%28%288%29%29

%28n-1%29log%28%281.5%29%29%3E3-log%28%288%29%29

n-1%3E%283-log%28%288%29%29%29%2Flog%28%281.5%29%29

n%3E%283-log%28%288%29%29%29%2F%28log%28%281.5%29%29%29%2B1

n=12.90808689

So the next integer is 13

You can substitute and find that the 13th term is 1037.971

And that is the least term of the sequence greater than 1000
because the 12th term is only 691.980

Edwin