Find the sum of 8 terms of the G.P. 3,6,12,24,..... .
To find the sum of the first n terms of a geometric progression (G.P.), we can use the formula:
S_n = a(1 - r^n) / (1 - r),
where:
S_n = sum of the first n terms,
a = first term of the G.P.,
r = common ratio of the G.P.
In this case, we need to find the sum of 8 terms. Let's plug in the given values:
a = 3 (first term),
r = 6 / 3 = 2 (common ratio when each term is divided by the previous term),
n = 8 (number of terms).
Now, we can substitute these values into the formula:
S_8 = 3(1 - 2^8) / (1 - 2).
Calculating this expression, we get:
S_8 = 3(1 - 256) / (1 - 2).
Simplifying further, we have:
S_8 = 3(-255) / (-1).
Finally, evaluating this, we get:
S_8 = 765.
Therefore, the sum of the first 8 terms of the G.P. 3, 6, 12, 24, ... is 765.