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
answer=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
answer=b
3)Find the two arithmetic means between 4 and 22
a.10,16
b.8,16
c.8,12
d.13,13
answer=a
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
answer=b
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
answer=d
1) To find the 20th term of an arithmetic sequence, you can use the formula: an = a1 + (n-1)d, where "an" is the nth term, "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:
a20 = 3 + (20-1)7
a20 = 3 + 19*7
a20 = 3 + 133
a20 = 136
So, the 20th term of the arithmetic sequence is 136. Therefore, the correct answer is b) 136.
2) To write an equation for the nth term of an arithmetic sequence, you can use the formula: an = a1 + (n-1)d, where "an" is the nth term, "a1" is the first term, "d" is the common difference, and "n" is the term number.
In this case, the first term is -3, and the common difference is 6 (as each term is increasing by 6). Plugging these values into the formula:
an = -3 + (n-1)6
an = -3 + 6n - 6
an = 6n - 9
Therefore, the equation for the nth term of the arithmetic sequence is an = 6n - 9. Therefore, the correct answer is b) an = 6n + 9.
3) To find the two arithmetic means between two terms of an arithmetic sequence, you can use the formula: (term1 + term2) / 2 = arithmetic mean.
In this case, the given terms are 4 and 22.
First, find the common difference by subtracting the first term from the second term: d = 22 - 4 = 18.
Next, find the first mean by adding half of the common difference to the first term: 4 + (1/2) * 18 = 4 + 9 = 13.
Finally, find the second mean by adding half of the common difference to the first mean: 13 + (1/2) * 18 = 13 + 9 = 22.
Therefore, the two arithmetic means between 4 and 22 are 13 and 22. So, the correct answer is d) 13, 13.
4) To find the sum (Sn) of an arithmetic series, you can use the formula: Sn = (n/2)(a1 + an), where "Sn" is the sum of the first "n" terms, "a1" is the first term, and "an" is the nth term.
In this case, a1 = 3, d = 1/2, and an = 15. To find "n," we can use the formula for the nth term of an arithmetic sequence: an = a1 + (n-1)d.
15 = 3 + (n-1)(1/2)
15 = 3 + (n/2) - (1/2)
15 - 3 = (n/2) - (1/2)
12 = (n/2) - (1/2)
12 + (1/2) = n/2
n/2 = 25/2
n = 25
Now, we can calculate the sum:
Sn = (n/2)(a1 + an)
Sn = (25/2)(3 + 15)
Sn = (25/2)(18)
Sn = 25*9
Sn = 225
Therefore, the sum of the arithmetic series is 225. So, the correct answer is a) 225.
5) This question involves sigma notation where "8" is on top of the sigma notation, and the expression "40-3k" is on the right side. The values of "k" start from 3 and increase by 1 for each term.
By plugging in the values of "k" into the expression "40-3k" and summing them up, we can find the answer.
When k = 3, the expression becomes: 40 - 3 * 3 = 40 - 9 = 31
When k = 4, the expression becomes: 40 - 3 * 4 = 40 - 12 = 28
When k = 5, the expression becomes: 40 - 3 * 5 = 40 - 15 = 25
And so on, following this pattern.
Adding up all these values, we get: 31 + 28 + 25 + ... + (add more terms)
By calculating this sum, you can determine which option is correct based on the given choices.
However, without the complete information of the terms involved, it is not possible to provide a specific answer.