Find the sum of the first five terms of the G.P. 2,6,18
To find the sum of the first five terms of a geometric progression (G.P.), we use the formula:
S = a(r^n - 1) / (r - 1)
where:
S = sum of the first n terms
a = first term
r = common ratio
n = number of terms
In this case, the first term (a) is 2, the common ratio (r) is 6/2 = 3, and we want to find the sum of the first 5 terms (n = 5).
Plugging these values into the formula:
S = 2(3^5 - 1) / (3 - 1)
S = 2(243 - 1) / 2
S = (2 * 242) / 2
S = 242
Therefore, the sum of the first five terms of the G.P. 2, 6, 18 is 242.