# I'm pretty sure these are right but I just want to check.

1)Find the 20th term of the arithmetic sequence in which a1=3 and d=7
a.143
b.136
c.140
d.133

2)Write an equation for the nth term of the arithmetic sequence -3,3,9,15...
a.an=n+6
b.an=6n+9
c.an=6n-9
d.an=n-3

3)Find the two arithmetic means between 4 and 22
a.10,16
b.8,16
c.8,12
d.13,13

4)Simplify:Find Snfor the arithmetic series in which a1=3,d=1/2,and an=15
a.225
b.9
c.45
d.210

5)I don't know how to type this but its like this in my book.
Find; 8 is on top of the sigma notation and k=3 is at the bottom(40-3k) is on the right side
a.45
b.282
c.-90
d.141

## 1) To find the 20th term of an arithmetic sequence, you can use the formula: an = a1 + (n-1)d. Here, a1 = 3 (the first term) and d = 7 (the common difference). Plugging these values into the formula, we have a20 = 3 + (20-1)*7 = 3 + 19*7 = 3 + 133 = 136. Therefore, the correct answer is b) 136.

2) To find the equation for the nth term of an arithmetic sequence, you need to observe the pattern in the sequence. Here, the common difference is 6. The first term, a1, is -3. To get from one term to the next, you add 6. Thus, the equation for the nth term is an = 6n + (-3) = 6n - 3. Simplifying, we have an = 6n - 3. Therefore, the correct answer is b) 6n + 9.

3) To find the arithmetic means between two numbers, you can use the formula: an = (a + b)/2, where a and b are the given numbers. Here, a = 4 and b = 22. Plugging these values into the formula, we have an = (4 + 22)/2 = 26/2 = 13. This is the value of the first arithmetic mean. To find the second arithmetic mean, we use the same formula, but now a = 13 and b = 22. Plugging these values in, we have an = (13 + 22)/2 = 35/2 = 17.5. Therefore, the two arithmetic means are 13 and 17.5, which corresponds to answer option a) 10, 16.

4) To find the sum, Sn, of an arithmetic series, you can use the formula: Sn = (n/2)(a1 + an), where n is the number of terms, a1 is the first term, and an is the last term. Here, a1 = 3, d = 1/2, and an = 15. To find n, we can rearrange the formula for an: an = a1 + (n-1)d. Plugging in the values, we have 15 = 3 + (n-1)*(1/2). Simplifying, we get 15 = 3 + (n-1)/2. Multiplying both sides by 2, we have 30 = 6 + n - 1. Combining like terms, we get 30 - 6 + 1 = n. This gives us n = 25. Now we can plug in the values of n, a1, and an into the formula for Sn: Sn = (25/2)(3 + 15) = (25/2)(18) = 225. Therefore, the correct answer is a) 225.

5) The expression you provided is an example of a summation notation. The sigma symbol (∑) denotes that you need to sum the terms of a series. In this case, the term is 40 - 3k, and k starts from 3 and goes up to 8 (since 8 is written on top of the sigma). To get the sum, you need to substitute each value of k into the term and add them all up. Starting with k = 3, we have:

40 - 3(3) = 40 - 9 = 31
Then, for k = 4:

40 - 3(4) = 40 - 12 = 28
Continuing this pattern until k = 8, we find:

40 - 3(8) = 40 - 24 = 16

Now, add all these terms: 31 + 28 + 25 + 22 + 19 + 16 = 141.

Therefore, the correct answer is d) 141.