find the sum of the first terms of the G.P. 2,6,18
To find the sum of the first n terms of a geometric progression, we can use the formula:
Sn = a * (1 - r^n) / (1 - r)
where:
Sn is the sum of the first n terms
a is the first term of the G.P.
r is the common ratio
n is the number of terms
In this case, the first term (a) is 2, the second term is 6, and the third term is 18. To find the common ratio (r), we can divide the second term by the first term, or the third term by the second term:
r = 6 / 2 = 3
Now, we need to find the sum of the first 3 terms:
Sn = 2 * (1 - 3^3) / (1 - 3)
Sn = 2 * (1 - 27) / -2
Sn = 2 * (-26) / -2
Sn = -52
Therefore, the sum of the first 3 terms of the G.P. 2, 6, 18 is -52.