Question

Find an equation for the nth term of the arithmetic sequence.

a10 = 32, a12 = 106

Answer 1

Firstly, the formula of for a term of an arithmetic sequence is given by:\[x _{n}=a+(n-1)d\]Where a is the first term, n is the term number, d is the common difference.

Since we know this is an arithmetic sequence, then a11 is the average of a10 and 12. Therefore:

a11 = (32 + 106) / 2
= 138 / 2
= 69

Now we have the sequence: 32, 69, 106. Since this is an arithmetic sequence, a11 - a10 gives us the common difference. d = 69 - 32 = 37. Now we got d, so we just need to find a. We can use the already given a11 to find a.\[69=a+(11-1)37 \rightarrow 60=a+370 \rightarrow a=-310\]Now we know a = -310 and = 37. We plug in these values to get the equation:\[x _{n}=-310+(n-1)37\]

Answer 2

oh i get it! thank you!

Answer 3

could you help me on this to? if you can

A certain species of tree grows an average of 3.1 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 400 centimeters tall.

Answer 4

A certain species of tree grows an average of 3.1 cm per week.
\[ d = 3.1\]the measurements begin when the tree is 400 centimeters tall.
\[a_1 = 400 \]So this means \[
a_n = a_1 +(n-1)d = 400+(n-1)3.1
\]

Answer 5

Ohh okay!
i just couldnt figure out how to start it!! thank you!!

Answer 6

also, for this problem; Find an equation for the nth term of the arithmetic sequence.

-3, -5, -7, -9, ...
would the answer be an = -3 + -2(n - 1)?

Answer 7

Yes.

Answer 8

okay! thank you

Answer 9

im sorry to be a bother.. but would this one be correct to?
Find an equation for the nth term of the arithmetic sequence.

8, 6, 4, 2, ...

an = 8 + -2(n - 1)?

Answer 10

Yeah

Answer 11

okay! thank-you!

Answer 12

a1=-1,d=-3,n=10 9th term?