The sum of the first 6 terms of a geometric series is 15,624 and the common ratio is 5 what is the first term of the serious?

Mathematics

1 answer:

kap26 [50]3 years ago

5 0

Answer:

first term = 4

Step-by-step explanation:

Sₙ = (a₁ * (1 - rⁿ)) / (1 - r) a₁: first term r: common ratio n: terms

15624 = (a₁ * (1 - 5⁶)) / (1 - 5)

= (a₁ * -15624) / -4

a₁ x (-15624) =15624 x (-4)

a₁ = 4

check: 4+20+100+500+2500+12500 =15624

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. Shanice is making a garden. The area of the garden is 24 ft2. Use the following shape and information to find the base (6−4) a

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Answer:

The base and height of the garden are 4.60 ft and 5.60 ft.

Step-by-step explanation:

The area of the garden is, A = 24 ft².

The base height of the garden are:

base (b) = 6x - 4

height (h) = x + 3

Compute the value of x as follows:

$A=\frac{1}{2}\times b \times h\\\\24=\frac{1}{2}\times (6x-4) \times (x+3)\\\\48=6x^{2}+18x-4x-12\\\\6x^{2}+14x-60=0\\\\3x^{2}+7x-30=0\\$

The last equation is a quadratic equation.

Compute the roots of the quadratic equation as follows:

$x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }\\x = \frac{ -14 \pm \sqrt{14^2 - 4(3)(-30)}}{ 2(3) }\\x = \frac{ -14 \pm \sqrt{556}}{ 6 }\\x = \frac{ -14 }{ 6 } \pm \frac{2\sqrt{139}\, }{ 6 }\\x = -\frac{ 7}{ 3 } \pm \frac{ \sqrt{139}\, }{ 3 }\\x = 1.59661\\x\approx 1.60$