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.