132k views
0 votes
9) Find a11 in an arithmetic sequence where a1 = −15 and a8 = 34

10) Find the arithmetic mean of the sequence -10,___,___,___,18

User Ellrohir
by
8.1k points

1 Answer

4 votes
9) In an arithmetic sequence, each term is found by adding a common difference (d) to the previous term. We can use this fact to find a11.

From the given information, we know that a1 = -15 and a8 = 34. We can use the formula for the nth term in an arithmetic sequence to find d:

a8 = a1 + (n-1)d
34 = -15 + 7d
49 = 7d
d = 7

Now that we know d, we can use the formula for the nth term to find a11:

a11 = a1 + (n-1)d
a11 = -15 + 10d
a11 = -15 + 10(7)
a11 = 55

Therefore, a11 in the arithmetic sequence is 55.

10) To find the arithmetic mean (or average) of the sequence -10, ____, ____, ____, 18, we need to find the three missing terms.

We can use the fact that the sequence is arithmetic to find the common difference (d):

d = a2 - a1 = a3 - a2 = a4 - a3 = a5 - a4

We can see that the common difference is d = 28/3 or approximately 9.33.

To find the missing terms, we can add d to the previous term:

a2 = -10 + d = -10 + 28/3 = -2.67
a3 = a2 + d = -2.67 + 28/3 = 5.67
a4 = a3 + d = 5.67 + 28/3 = 13
a5 = a4 + d = 13 + 28/3 = 20.33

Now that we have all the terms, we can find the arithmetic mean:

mean = (a1 + a2 + a3 + a4 + a5)/5
mean = (-10 - 2.67 + 5.67 + 13 + 20.33)/5
mean = 5.4

Therefore, the arithmetic mean of the sequence is 5.4.
User Perfume
by
7.6k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories