## katherinekc 2 years ago Find an equation for the nth term of the arithmetic sequence. a10 = 32, a12 = 106

1. genius12

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:$x _{n}=-310+(n-1)37$

2. katherinekc

oh i get it! thank you!

3. katherinekc

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.

4. wio

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 $a_n = a_1 +(n-1)d = 400+(n-1)3.1$

5. katherinekc

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

6. katherinekc

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)?

7. wio

Yes.

8. katherinekc

okay! thank you

9. katherinekc

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)?

10. wio

Yeah

11. katherinekc

okay! thank-you!

12. 3p0huggedout

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