How do you solve for b in this expression

Mathematics

1 answer:

Leona [35]3 years ago

7 0

Remember you can do anything to an equation as long as you do it to both sides

8-(3+b)=b-9

remember the distributive property
a(b+c)=ab+ac

distribute that invisible -1
-(3+b)=-1(3+b)=-1(3)-1(b)=-3-b

8-3-b=b-9
add like terms
5-b=b-9
add b to both sides
5=2b-9
add 9 to both sides
14=2b
divide both sides by 2
7=b
b=7

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The 13th term of a geometric sequence is 16, 384 and the first term is 4. What is the common ratio?

AleksAgata [21]

Answer:

$\large \boxed{2}$

Step-by-step explanation:

The formula for the nth term of a geometric sequence is

aₙ = a₁rⁿ⁻¹

In your geometric sequence, a₁ = 4 and a₁₃ = 16 384.

$\begin{array}{rcl}16384 & = & 4r^{(13 - 1)}}\\16384 & = & 4r^{12}\\4096 & = & r^{12}\\3.6124 & = & 12 \log r\\0.30102 & = & \log r\\r & = & 10^{0.30102}\\ & = & \mathbf{2}\\\end{array}\\\text{The common ratio is $\large \boxed{\mathbf{2}}$}$