An arithmetic sequence with a third term of 8 and a constant difference of 5.

1 answer:

8 0

An arithmetic sequence (a_n) is as follows:

$a_1\\a_2=a_1+d\\a_3= a_1+2d\\a_4=a_1+3d,...$ where $a_1$ is the first term and d is the constant difference,

thus, we see that the n'th term of an arithmetic sequence is $a_n=a_1+(n-1)d$

in our particular case d=5, the third term is 8, so we have:

$a_3=8=a_1+2\cdot5\\\\8=a_1+10\\\\a_1=-2$

and the general term is $a_n=-2+5(n-1)$ ,

Answer: first term is -2, n'th term is -2+5(n-1)

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PLEASE HELP<br> what is 30th term of -12, -3, 6, 15

hoa [83]

Answer:

249

Step-by-step explanation:

We can see that the difference of every term in the given sequence is 9, because -12 + 9 = -3, -3 + 9 = 6 and 6 + 9 = 15. We may therefore assume that the sequence is <em>arithmetic </em>(a fancy word of saying that a sequence is increasing with a constant value every term).

Since the difference of every term is 9, we know that the explicit form of the sequence (where the value of every term is expressed in terms of the term number) is in the form $9n+c$ , where $n$ is the term number and $c$ is a constant we are going to figure out right now.

We know that the first term of the sequence is -12, so we see that $9(1) + c = -12$ and hence $c=-21$ . Therefore, the 30th term of the sequence is $9(30) - 21 = 249$ .

5 0

3 years ago

Multiply the additive inverse of (-7/8) by the reciprocal of (5 1/2)<br><br>PLEASE HELP!

EleoNora [17]

Answer:

$\bold {$\dfrac{7}{44}$}$

Step-by-step explanation:

<h3> Reciprocal:</h3>

$\sf \text{The reciprocal of any number $\dfrac{a}{b}$ is given by $\dfrac{b}{a}$}\\\\5\dfrac{1}{2}=\dfrac{11}{2}\\\\\text{Reciprocal of $\dfrac{11}{2}$ = $\dfrac{2}{11}$}$