3(q-7)=27 solve for q

Mathematics

2 answers:

Zanzabum3 years ago

8 0

Answer:

q =16

Step-by-step explanation:

q - 7 = 27/3

q = 9 + 7

q = 16

Best regards

Naddik [55]3 years ago

7 0

Q = 16

First, divide both sides o the equation by 3.

q - 7 = 27 / 3

q - 7 = 9

Now, add 7 on both sides.

q = 16

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where $d$ is the common difference between terms. You can solve for $a_n$ in terms of any of the previous terms of the sequence:

$a_n=a_{n-1}+d\implies~a_n=a_{n-2}+2d\implies~a_n=a_{n-3}+3d\implies\cdots\implies~a_n=a_{n-k}+kd$

for some integer $1\le k\le n-1$

Continuing in this way, you know that the sequence can be defined explicitly in terms of the first term $a_1$

$a_n=a_1+(n-1)d$

Given that the 4th term is $a_4=-6$ and the 11th term is $a_{11}=-34$ , you have the following system of equations.

$\begin{cases}-6=a_1+(4-1)d\\-34=a_1+(11-1)d\end{cases}$

Solving this system for the two unknowns yields $a_1=6$ and $d=-4$ .

So, the sequence is given explicitly by

$a_n=6+(n-1)(-4)=-4n+5$