In a gp if t3 = 18 and t6 = 486 find: - t10

The 10th term of the G.P is 29.              

Step-by-step explanation:

Given : In a GP if and .

To find : The term ?

Solution :

The geometric sequence is in the form,

Where, a is the first term and r is the common ratio.

The nth term of G.P is

We have given,

i.e.

....(1)

i.e.

....(2)

Solving (1) and (2) by dividing them,

Substitute in (1),

The first term is a=2 and the common ratio is r=3.

The 10th term, of GP is given by,

Therefore, The 10th term of the G.P is 29.

T10=39366

Step-by-step explanation:

In geometric progression, third term is 18 and 6th term is 486

we need to find out 10th term

In geometric progression , nth term is

where r is the common ratio and T_1 is the first term

T3= 18 and T6= 486

Divide second equation by first equation

Take cube root on both sides

r= 3

, plug in 3 for 'r'

Divide by 9 on both sides

t1= 2

So T1=2  and r=3

T10=39366