Answer:
Ai. Common ratio = 2/3
Aii. First term = 54
B. Sum of the first five terms = 422/3
Step-by-step explanation:
From the question given above, the following data were obtained:
3rd term (T3) = 24
6Th term (T6) = 64/9
First term (a) =?
Common ratio (r) =?
Sum of the first five terms (S5) =?
Ai. Determination of the common ratio (r).
T3 = ar²
T3 = 24
24 = ar²....... (1)
T6 = ar⁵
T6 = 64/9
64/9 = ar⁵......... (2)
The equation are:
24 = ar²....... (1)
64/9 = ar⁵......... (2)
Divide equation 2 by equation 1.
64/9 ÷ 24 = ar⁵ / ar²
64/9 × 1/24 = r³
8/27 = r³
Take the cube root of both side
r = 3√(8/27)
r = 2/3
Thus, the common ratio is 2/3
Aii. Determination of the first term (a).
T3 = ar²
3rd term (T3) = 24
Common ratio (r) = 2/3
First term (a) =?
24 = a(2/3)²
24 = 4a/9
Cross multiply
24 × 9 = 4a
216 = 4a
Divide both side by 4
a = 216/4
a = 54
Thus, the first term (a) is 54
B. Determination of the sum of the first five terms.
Common ratio (r) = 2/3
First term (a) = 54
Number of term (n) = 5
Sum of first five terms (S5) =?
Sn = a[1 –rⁿ] / 1 – r
S5 = 54[1 – (⅔)⁵] / 1 – ⅔
S5 = 54 [1 – 32/243] / ⅓
S5 = 54 (211/243) × 3
S5 = 54 × 211/81
S5 = 6 × 211/9
S5 = 2 × 211/3
S5 = 422/3
Thus, the sum of the first five terms is 422/3
C. This is because if it is an equiangular triangle this means that all the angles have the same angle. You know that all the angles in a triangle add up to 180 degrees? You just divided 180 by 3 as there are three angles in a triangle. Which gives you 60 degrees.
Answer:
508%
Step-by-step explanation:
To change to a percent multiply by 100
5.08 * 100
508%
Answer:
(f+g)(x)= 3x^2 -2x-1
Step-by-step explanation:
f(x) = -4x+3
g(x) = 3x^2+2x-4
(f+g)(x)= -4x+3 +3x^2+2x-4
Combine like terms
(f+g)(x)= 3x^2 -2x-1
Answer:
a) x = 260
b) g = 218
c) z = 30
d) h = 5
Step-by-step explanation:
a)
Predict a number; let's say x = 225
Too low; try with a higher number; let's say x = 270
Too high, we're closer.
x = 260
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b)
let's say g = 230
Too high. Try g = 221
We're almost there. Let's try with g = 218
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c)
Let's try with z = 15
Too low; try a higher number. z = 30
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d)
Let's try with h = 6
Too high; let's try with h = 5