If the first second and last term of a G.P are 4, _20 and _12500 respectively find the number of terms in the G.P

Answer 1

Let the common ratio of the G.P be denoted by r.

We know that the first term is 4, so we can write:

a₁ = 4

We also know that the second term is -20, so we can write:

a₂ = 4r = -20

Solving for r, we get:

r = -5

Now we can find the nth term of the G.P using the formula:

aₙ = a₁ * r^(n-1)

We know that the last term is 12500, so we can write:

12500 = 4 * (-5)^(n-1)

Simplifying, we get:

3125 = (-1)^(n-1) * 5^(3-n)

Taking the logarithm of both sides, we get:

log(3125) = (3-n) * log(5)

Solving for n, we get:

n = 6

Therefore, there are 6 terms in the G.P.