Find the sum of the first eight terms of the G.P 2,6,18,54...
As with all GPs,
Sn = a(r^n - 1)/(r-1)
So plug in your numbers.
Find the sun of the eight term of the G.P2,6,18
I need answer to the question
Given GP as 2, 6, 18,......, find the eight term of the GP
To find the sum of the first eight terms of a geometric progression (G.P), you can use the formula:
Sum of n terms of a G.P = a * (r^n - 1) / (r - 1),
where
a = first term of the G.P,
r = common ratio of the G.P,
n = number of terms of the G.P.
In this case, we are given the G.P 2, 6, 18, 54..., and we need to find the sum of the first eight terms.
First, let's find the first term, a. From the given G.P, we can see that the first term is 2.
Next, let's find the common ratio, r. To find the common ratio, we can divide any term by the preceding term. By dividing each term by its preceding term, we can observe that each term is three times the previous term:
6 / 2 = 3,
18 / 6 = 3,
54 / 18 = 3,
...
Therefore, we can conclude that the common ratio, r, is 3.
Now, let's find the sum of the first eight terms of the G.P:
n = 8, a = 2, r = 3.
Using the formula mentioned earlier:
Sum of n terms of a G.P = a * (r^n - 1) / (r - 1)
= 2 * (3^8 - 1) / (3 - 1)
Now, we can calculate the sum:
Sum of first eight terms = 2 * (6561 - 1) / 2
= 2 * 6560 / 2
= 6560
Therefore, the sum of the first eight terms of the G.P 2, 6, 18, 54... is 6560.