Double the second number, the sum is 34."

A geometric progression has a third term of 20 and a sum of infinity which is 3 times the first term. Find the first term

Anna007 [38]

Answer: the first term is 45

Step-by-step explanation:

Step 1: The formular for the nth term is ar^n-1 and since we're solving for the third term ar^3-1 = ar² which is equal to 20

So ar²= 20 and we make this equation i

Step 2: the formular for the sum of infinity is Sn = a/(1-r) and according the question the sum of infinity is equals to 3 *A ( A means the first term)

Further simplification gives us

3a= a/(1-r)

We simplify Futher by multiplying both sides by (1-r)

3a.(1-r) = a/(1-r).(1-r)

3a(1-r)=a

= 3a-3ar=a

Make 3ar the subject of the formula

3ar= 2a and lets make this equation (ii)

Step 3: From the first equation since ar²=20, let's make a the subject of the formula by dividing both sides by r²

Ar²/r² = 20/r²

A=20/r²lets make this equation (iii)

Step 4: subtitle a as 20/r² into equation (ii)

Since 3ar=2a

Then 3.(20/r²).r = 2. 20/r²

= (60/r²) .r = 40/r²

60/r = 40/r2

Multiplying both sides by r² gives us

60r = 40

Divide both sides by 20 gives us

= 3r= 2

Divide both sides by 3 gives us

= r = 2/3

Step 5: substitute r for 2/3 in equation i

ar²= 20

a. (2/3)2 = 20

= a.4/9 = 20

= 4a = 180

= a = 180/4

a = 45

5 0

4 years ago

7th grade math pls help

katen-ka-za [31]

Answer:

25.12

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

A medical study investigated the effect of calcium and vitamin supplements on the risk of older Americans for broken bones. A to

timofeeve [1]

Answer:

$\frac{37}{389}$

Step-by-step explanation:

Given that a medical study investigated the effect of calcium and vitamin supplements on the risk of older Americans for broken bones. A total of 389 older Americans who lived at home and were in good health were studied over a three-year period. While all of the 389 people took in at least 700 milligrams of calcium and 200 units of vitamin D through their normal diet, 187 of them were given additional supplements containing 500 milligrams of calcium citrate and 70 units of vitamin D daily. Of the 187 who took additional supplements, 11 of them suffered broken bones over the three-year period. Of the 202 older Americans who did not take the additional supplement, 26 of them suffered broken bones over the study period.

Group I Group II Total

n 187 202 389

favour x 11 26 37

The fraction of older Americans who were included in the study suffered broken bones during the three-year period

=Total x/total n

= $\frac{37}{389}$

4 0

3 years ago

Formula for the volume of a square pyramid, v=1/3lwh for w

tatuchka [14]

$\dfrac{1}{3}lwh=V\qquad|\text{multiply both sides by 3}\\\\lwh=3V\qquad|\text{divide both sides by}\ lh\neq0\\\\\boxed{w=\dfrac{3V}{lh}}$

3 0

4 years ago

Helpppppp Asap!!!!!! The question is in the picture

Dominik [7]

The approximate length of side AB is 14.0. The correct option is B. 14.0 units

<h3>Law of sines </h3>

From the question, we are to determine the measure of side AB

First, we will determine the measure of angle A

A + B + C = 180° (<em>Sum of angles in a triangle</em>)

A + 65° + 35° = 180°

A = 180° - 65° - 35°

A = 80°

Now, using the law of sines

c/sinC = a/sinA

c = AB

a = BC = 24

Thus,

c/sin35° = 24/sin80°

c = (24×sin35°)/sin80°

c = 13.978

c ≈ 14.0

∴ AB = 14.0

Hence, the approximate length of side AB is 14.0. The correct option is B. 14.0 units

Learn more on Law of sines here: brainly.com/question/24138896

#SPJ1

4 0

2 years ago