Mathematics, 05.05.2020 04:28, bbrogle4070

If you are good at arithmetic sequences in math please help I am giving more points

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answered: crawford184232323234

a_n=-5n+106

Step-by-step explanation:

Arithmetic sequences are linear.

Let's find the slope.

$\frac{a_{16}-a_{7}}{16-7}=\frac{26-71}{16-7}=\frac{-45}{9}=-5$ .

So the slope is -5.

We know this about our equation:

a_n=-5n+b

We need to find .

Let's use a point on the line like (7,71) .

Input the point into our equation:

71=-5(7)+b

71=-35+b

Add 35 on both sides:

106=b

The equation for this line/arithmetic sequence is:

a_n=-5n+106 .

answered: mathman783

$a_{n} =101+(n-1)(-5)$

Step-by-step explanation:

Let's start by finding the common difference of this arithmetic sequence.

The change from $a_{7}$ to $a_{16}$ is -45 because it decreased 45.

$a_{16}$ is 9 terms away from $a_{7}$ .

If we divide the change by the difference in n, then we can find the difference between each term, or the common difference.

-45/9 = -5, so the common difference is -5.

Now, we want to find $a_{1}$ .

We can do this using the common difference. Subtracting the common difference from $a_{7}$ six times should tell us what $a_{1}$ is, so let's do that.

$a_{1}$ = 71 - (-5) - (-5) - (-5) - (-5) - (-5) - (-5)

A reminder, subtracting a negative is basically the same as adding it.

$a_{1}$ = 71 + 5 + 5 + 5 + 5 + 5 + 5

$a_{1}$ = 101

With the common difference and $a_{1}$ , we now have all the parts we need to write a rule for the nth term of this sequence.

The formula for the nth term of a sequence is

$a_{n} =a+(n-1)d$ , with $a_{n}$ being the nth term, a being $a_{1}$ , and d being the common difference.

We can just substitute the common difference and a to get our formula.

$a_{n} =101+(n-1)(-5)$

answered: Guest

step-by-step explanation:

answered: Guest

step-by-step explanation:

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If you are good at arithmetic sequences in math please help I am giving more points
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