Question 1210345
<pre>
I'll assume the student meant

THE 2ND AND 7TH TERM OF A G.P ARE 18 AND 4374 RESPECTIVELY. FIND THE 
1) COMMON RATIO 
2) FIRST TERM 
3) SUM OF THE 4TH AND 8TH TERM
4) SUM OF THE FIRST 10 TERMS

1) COMMON RATIO 


{{{a[1]=a*r^(2-1)=ar=18}}}
{{{a[7]=a*r^(7-1)=ar^6=4374}}}

Divide the second equation term-by-term by the first equation.

{{{(a[6]r^6)/(a[1]r)=4374/18}}}

{{{r^5=243}}}

{{{r = root(5,243)}}}

{{{r = 3}}}

2) FIRST TERM 

{{{a[1]r=18}}}
{{{a[1]*3=18}}}
{{{a[1]=18/3}}}
{{{a[1]=6}}}

3) SUM OF THE 4TH AND 8TH TERM

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

{{{a[4]=a[1]*r^(4-1)=6*3^3=6*27=162}}}

{{{a[8]=a[1]*r^(8-1)=6*3^7=6*2187=13122}}} 

{{{a[4]+a[8]= 162+13122=13284}}}

4) SUM OF THE FIRST 10 TERMS

{{{S[n]=a[1]*expr((r^n-1)/(r-1)))}}}

{{{S[10]=6*expr((3^10-1)/(10-1))=6*expr((59049-1)/(9))=6*expr((59048)/(9))=6*29524=177144}}}

Edwin</pre>