Question

The 4th and 10th term of an gp are 1/3 and 243 respectively find the 2nd term

Answer 1

Step-by-step explanation:

which is the required ans.

Answer 2

Answer:

The 2nd term of the G.P is $\frac{1}{27}$

Step-by-step explanation:

We have been given 4th term of G.P i.e $\frac{1}{3}$

and also 10th term of the G.P i.e 243

Let the 1st term of the G.P be a and common ratio be r

Therefore 4th term $ar^{3}=\frac{1}{3}$ .....(i)

10th term $ar^{9}=243$ .......(ii)

Now we will find common ratio r

Therefore Dividing Equation(ii) by Equation(i) we get

$\frac{ar^{9}}{ar^{3}}=\frac{243}{\frac{1}{3}}$

$r^{6}=243\times 3$

$r^{6}=729$

$r=3$

Therefore common ratio r=3

Now we have to find the first term a

Putting the value of r in equation we get

$a3^{3}=\frac{1}{3}$

$27a=\frac{1}{3}$

$a=\frac{1}{81}$

$\textrm{Therefore first term a=}\frac{1}{81}$

Now we have to find the 2nd term i.e ar

Putting the value of a and r we get

$\frac{1}{81}\times 3=\frac{1}{27}$

Therefore,2nd term is$\frac{1}{27}$