a geometric progression is given as 8/81-4/27+2/9.find the sum of the first five terms.
Check to see that the value of r = 3/2 , that is ...
(-4/27) ÷ (8/81) and (2/9) ÷ (-4/27) = -3/2
so a = 8/81, and r = -3/2
sum(n) = a(1 - r^n)/(1-r)
sub in the values and evaluate, let me know what you got
plz I don't understand very well explain further more.í ½í¹�í ½í¹�í ½í²�í ½í²�í ½í²�
To find the sum of the first five terms of a geometric progression, we'll first determine the common ratio (r) for the given series and use the formula for the sum of a geometric progression.
Given the geometric progression: 8/81, -4/27, +2/9
To find the common ratio (r), we divide any term by its preceding term:
-4/27 ÷ 8/81 = (-4/27) * (81/8) = -324/216 = -3/2
Now we have the first term (a) = 8/81 and the common ratio (r) = -3/2.
The formula for the sum of a geometric progression is:
S_n = a * (1 - r^n) / (1 - r)
In this case, we want to find the sum of the first five terms (n = 5). Plugging in the values, we get:
S_5 = (8/81) * (1 - (-3/2)^5) / (1 - (-3/2))
To simplify this further, we can calculate (-3/2)^5 = -243/32:
S_5 = (8/81) * (1 - (-243/32)) / (1 + 3/2)
= (8/81) * (1 + 243/32) / (5/2)
= (8/81) * (313/32) / (5/2)
Multiplying the fractions:
S_5 = (8*313) / (81*32) * (2/5)
= 5024 / 2592
= 13/27
Therefore, the sum of the first five terms of the given geometric progression is 13/27.