find the sum of the 8th term of the G.P 6,9,12,15 and 18.
To find the sum of the 8th term of a geometric progression (G.P.), we need to first determine the common ratio (r).
In a geometric progression, each term is obtained by multiplying the previous term by a constant factor, which is the common ratio (r). To find the common ratio, we can divide any term by its preceding term.
In this case, let's divide the second term (9) by the first term (6):
r = 9 / 6 = 1.5
Now that we know the common ratio, we can find the formula for the nth term of a geometric progression:
nth term (Tn) = a * r^(n-1)
Where:
Tn = The nth term of the G.P.
a = The first term of the G.P.
r = The common ratio of the G.P.
n = The position of the term we want to find.
Applying this formula, we can calculate the 8th term (T8) of the G.P.:
T8 = 6 * (1.5)^(8-1)
= 6 * 1.5^7
Now, let's compute the sum of the first 8 terms of the G.P. using the formula for the sum of n terms in a geometric progression:
Sum (S) = a * (1 - r^n) / (1 - r)
In our case, we want to find the sum of the first 8 terms, so n = 8. Substituting the values, we have:
S = 6 * (1 - 1.5^8) / (1 - 1.5)
Simplify this expression to find the sum of the 8 terms.
This is not a GP, but an AP, with
a=6
d=3
and T8 = a+7d ...