What is the number of the terms of geometrical sequence if its first, fourth and the last term is equal to 2, 54 and 486 respectively.

The number of terms of the G.P. is 6

Step-by-step explanation:

Let the G.P. has first term a, common ratio r and the number of terms n.

The G.P. has first term 2, so a = 2.

Now, the fourth term is 54 i.e. ar³ = 54

⇒ 2r³ = 54

⇒ r³ = 27

⇒ r = 3

Now, the last term i.e. the nth term is=

⇒

⇒

Hence, (n - 1) = 5

⇒ n = 6

So the number of terms of the G.P. is 6 (Answer)

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.