Question 991841
8, 12, 18, 27

(a) Find the formula for its general term.
<pre>
We find the common ratio by dividing each term after the
first by the preceding term

{{{12/8=3/2}}}, {{{18/12=3/2}}}, {{{27/18=3/2}}} 

So {{{r=3/2=1.5}}}

Use standard formula

{{{a[n]=a[1]r^(n-1) }}}

{{{a[n]=8(1.5)^(n-1)}}}
</pre>
(b) Find its 17th term to 3 significant 
    figures.
<pre>
Substitute 17 for n

{{{a[17]=8(1.5)^(17-1)}}}

{{{a[17]=5254.727}}}
</pre>
(c) Use algebra to find out which is the 
    least term of the sequence greater than 1000.
<pre>
{{{a[n]=8(1.5)^(n-1)>1000}}}

{{{log((8(1.5)^(n-1)))>log((1000))}}}

{{{log((8))+log((1.5)^(n-1))>3}}}

{{{log((1.5)^(n-1))>3-log((8))}}}

{{{(n-1)log((1.5))>3-log((8))}}}

{{{n-1>(3-log((8)))/log((1.5))}}}

{{{n>(3-log((8)))/(log((1.5)))+1}}}

{{{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</pre>