Given a geometric progression:
0.05, 0.2, 0.8, ... Find the sum from the 5th term to the 8th term?
That would be S8 - S4
Since r = 4
.05(4^8-1) - .05(4^4-1) = 3264
a=0.05
r=4
S8=0.05(4^8-1)/3=1092.25
S4=0.05(4^4-1)/3=4.25
Sum from 5th term to 8th term is
S8-S4=1088
To find the sum from the 5th term to the 8th term of a geometric progression, we first need to find the common ratio of the progression.
The common ratio (r) is found by taking the quotient of any term and its preceding term. Let's take the quotient between the 2nd and 1st terms:
r = 0.2 / 0.05 = 4
Now that we have the common ratio, we can use the formula for the sum of a geometric series to find the sum from the 5th to the 8th term. The formula is:
Sn = a * (r^n - 1) / (r - 1)
where:
Sn is the sum of the geometric series
a is the first term
r is the common ratio
n is the number of terms
In this case, the first term (a) is 0.05, the common ratio (r) is 4, and we want to find the sum from the 5th term to the 8th term, so n = 8 - 5 + 1 = 4.
Plugging in these values into the formula, we get:
S4 = 0.05 * (4^4 - 1) / (4 - 1)
Simplifying further:
S4 = 0.05 * (256 - 1) / 3
S4 = 0.05 * 255 / 3
S4 = 4.25
Therefore, the sum from the 5th term to the 8th term of the given geometric progression is 4.25.