The 6th term of a g.p is 64,if the first term is 2 find the common ratio

We know that the formula for the nth term of a geometric progression (G.P) is given by:

an = a1 * r^(n-1)

Given that the first term (a1) is 2 and the 6th term (a6) is 64, we can use the formula to find the common ratio (r):

a6 = a1 * r^(6-1)
64 = 2 * r^5

To isolate r, we can divide both sides by 2:

64/2 = r^5
32 = r^5

To find the value of r, we take the fifth root of both sides:

r = ∛(32)

Calculating the cube root of 32, we find:

r ≈ 2

Therefore, the common ratio (r) of the geometric progression is 2.