Question

The 6th term of a Gp is -2/27 and the first term is 18. what is the common ratio.

Answer 1

Answer:

Maths keeps one mentally active. The 3rd term of the GP is ar^2 = 18 and the 6th term, ar^5 = 486. a, the first term is 2 and the common ratio, r = 3.

Answer 2

Answer:

-1/3

Step-by-step explanation:

step 1:-  $n^{th}$ term of GP is $T_{n}$ = a*$r^{n-1}$   where  a = first term of GP & r =  common ratio

step 2:- From given data $6^{th}$ term is -2/27

             Hence ,  n = 6 ; $T_{6}$ = -2/27 ; a =18;

step 3 : -  $T_{n}$ = a*$r^{n-1}$  

              by replacing values

                $\frac{-2}{27}$ = 18*$r^{6-1}$ ;

                 $r^{5}$ = $\frac{-2}{27 * 18}$  ;

                  $r^{5}$ = $\frac{-1}{27 * 9}$   ;

                    $r^{5}$ = $\frac{-1}{243}$  ;

                   r = $\frac{-1}{3}$   ( As $3^{5}$ = 243 , divide both side by $5^{th}$ root)