3(q + 4/3) = 2 Solve for q

Mathematics

2 answers:

Fofino [41]4 years ago

6 0

Answer:

q = -2/3

Step-by-step explanation:

3(q + 4/3) = 2

1) Distribute

3q + 4 = 2

2) Isolate q

3q = -2

q = -2/3

Final answer: q = -2/3

trasher [3.6K]4 years ago

3 0

Answer: $q=-2/3$

Simplify both sides of the equation

$(3)(q)+(3)(3/4)=2$ $(Distribute)$

$3q+4=2$

Subtract 4 from both sides

$3q+4-4=2-4$

$3q=-2$

Divide both sides by 3

$3q/3=-2/3$

Final Answer: $q=-2/3$

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The sum of the series. Can you explain how to do? Thanks!

Doss [256]

Answer:

5115

Step-by-step explanation:

First of all, we need to assume there is a typo involved, and that the expression is supposed to be ...

$\displaystyle\sum_{i=1}^{10}{5\left(\dfrac{1}{2}\right)^i}$

The values being summed look a lot like the general term of a geometric sequence:

$a_1(r^{n-1})$

The exponents in the sum range from 1 to 10, so the values being summed range from 5/2 to 5/1024. In order for that to be the case with our general term, for r = 1/2, we must have a1 = 5/2 as we let n range from 1 to 10.

The sum of the terms of the geometric sequence is ...

$S_n=a_1\dfrac{1-r^n}{1-r}\\\\S_{10}=\dfrac{5}{2}\cdot\dfrac{1-\left(\dfrac{1}{2}\right)^{10}}{1-\dfrac{1}{2}}=\dfrac{5}{2}\cdot\dfrac{1023}{512}=\dfrac{5115}{1024}$