Hi I need someone to check my answers I'll show whatever work I have but for time purposes I'll just post my answers because I think I have most of them correct. Thanks!

1)Find the 20th term of the arithmetic sequence in which a1=3 and d=7.
A)143
B)136
C)140
D)133
I chose B

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
I chose B

3)Find the two arithmetic means between 4 and 22.
A)10,16
B)8,16
C)8,12
D)13,13
I chose A

4)Simplify: Find Sn for the arithmetic series in which a1=3,d=1/2,and aN=15
A)225
B)9
C)45
D)210
I chose B

5)ok this one's tricky to type but its with sigma so here it is.
There is a sigma sign and there is an 8 on the top of it and k=3 below. In parentheses to the right is (40-3k) and the question is Find.
A)45
B)282
C)-90
D)141
I chose D. this question is tricky but if you read it slowly and you know about sigma you'll be able to help. Thanks again.

Your #2 and 4 are not correct

#2:

you picked B which is tn = 6n+9
if you let n=1 you get 15 as your first term, you should obtain -3
doesn't C give you that result?

#4:

tn = 15
15 = 3 + (n-1)(1/2)
12 = (n-1)/2
24 = n-1
n=25

So S25 = 25/2[6 + 24(1/2)]
= 25/2[18]
= 225 which is A

ok thanks. Did you check the others?

the others were ok

Sure, I can check your answers for you. Let's go through each question and see if your choices are correct.

1) Find the 20th term of the arithmetic sequence in which a1 = 3 and d = 7.
To find the nth term of an arithmetic sequence, we use the formula: an = a1 + (n-1)d, where a1 is the first term, d is the common difference, and n is the term number.
In this case, a1 = 3, d = 7, and n = 20. Plugging these values into the formula, we get:
a20 = 3 + (20-1)*7
a20 = 3 + 19*7
a20 = 3 + 133
a20 = 136

Your answer of choice B) 136 is correct!

2) Write an equation for the nth term of the arithmetic sequence -3, 3, 9, 15...
To find the equation for the nth term of an arithmetic sequence, we can observe that the common difference between consecutive terms is 6 (3 - (-3) = 6). We can then use this common difference along with the formula an = a1 + (n-1)d.
In this case, a1 = -3, and d = 6. Plugging these values into the formula, we get:
an = -3 + (n-1)*6
an = -3 + 6n - 6
an = 6n - 9

Your answer of choice B) aN = 6n + 9 is incorrect. The correct answer is D) aN = n - 3.

3) Find the two arithmetic means between 4 and 22.
To find the arithmetic means between two numbers, we need to find the average of those two numbers. In this case, the two numbers are 4 and 22. We can find the first mean by adding both numbers and dividing by 2:
First mean = (4 + 22) / 2 = 26 / 2 = 13
Now, we can find the second mean by taking the average of the first mean (13) and 22:
Second mean = (13 + 22) / 2 = 35 / 2 = 17.5

So, the two arithmetic means between 4 and 22 are 13 and 17.5.

Your answer of choice A) 10, 16 is incorrect. The correct answer is D) 13, 13.

4) Simplify: Find Sn for the arithmetic series in which a1 = 3, d = 1/2, and aN = 15.
To find the sum of an arithmetic series, we 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.
In this case, a1 = 3, d = 1/2, and aN = 15. We need to find n to calculate the sum. We can use the formula aN = a1 + (n-1)d and solve for n:
15 = 3 + (n-1)(1/2)
15 = 3 + (n-1)/2
12 = (n-1)/2
24 = n-1
n = 25

Now, plugging in the values into the sum formula, we get:
Sn = (25/2)(3 + 15)
Sn = (25/2)(18)
Sn = 225

Your answer of choice B) 9 is incorrect. The correct answer is A) 225.

5) The notation with the sigma sign suggests that we need to evaluate a summation. The expression is โˆ‘(40 - 3k) from k = 3 to 8.
To solve this, we substitute the values of k from 3 to 8 into the given expression and sum them up:
โˆ‘(40 - 3k) = (40 - 3(3)) + (40 - 3(4)) + (40 - 3(5)) + (40 - 3(6)) + (40 - 3(7)) + (40 - 3(8))
= (40 - 9) + (40 - 12) + (40 - 15) + (40 - 18) + (40 - 21) + (40 - 24)
= 31 + 28 + 25 + 22 + 19 + 16
= 141

Your answer of choice D) 141 is correct!

So, out of the five questions, you got three correct (1, 3, and 5) and two incorrect (2 and 4). I hope this helps! Let me know if you have any further questions.