Please help me with my midterm review my teacher was out sick today and idk how much longer she will be but my midterms Thursday. She only helps people who she has seen done there midterm review and gotten over half of it right so can any of you please help me.
Write the first four terms of the sequence whose general term is given.
an = 3n - 1
Answer
2, 3, 4, 5
2, 5, 8, 11
-2, -5, -8, -11
4, 7, 10, 13
3 points
Question 2
Write the first four terms of the sequence whose general term is given.
an = 2(2n - 3)
Answer
-6, -2, 2, 6
-1, 1, 3, 5
-2, -4, -6, -8
-2, 2, 6, 10
3 points
Question 3
Write the first four terms of the sequence whose general term is given.
an = 4n
Answer
1, 16, 81, 256
4, 16, 64, 256
1, 4, 16, 64
16, 64, 256, 1024
3 points
Question 4
Write the first four terms of the sequence whose general term is given.
an = (2/3)n
Answer
1, , ,
, , ,
1, , ,
, , ,
3 points
Question 5
Write the first four terms of the sequence whose general term is given.
an = (-1)n(n + 5)
Answer
6, 7, 8, 9
-6, -14, -24, -36
-6, 7, -8, 9
-6, -7, -8, -9
3 points
Question 6
Write the first four terms of the sequence whose general term is given.
an = (-1)n + 1(n + 6)
Answer
-7, 8, -9, 10
-8, 9, -10, 11
7, -8, 9, -10
7, -16, 27, -40
3 points
Question 7
Write the first four terms of the sequence whose general term is given.
an =
Answer
4, , , 1
-4, , , 1
4, - , , 1
-4, - , , 1
3 points
Question 8
Write the first four terms of the sequence defined by the recursion formula.
a1 = -5 and an = an-1 - 3 for n ≥ 2
Answer
-5, - 4, - 1, 2
5, 2, -1, -4
-5, -8, -11, -14
5, 8, 11, 14
3 points
Question 9
Write the first four terms of the sequence defined by the recursion formula.
a1 = -6 and an = -2an-1 for n ≥ 2
Answer
6, -12, 24, -48
-6, 14, -26, 50
-6, -12, -24, -48
-6, 12, -24, 48
3 points
Question 10
Write the first four terms of the sequence defined by the recursion formula.
a1 = 4 and an = 3an-1 + 2 for n ≥ 2
Answer
4, 14, 44, 134
4, 10, 28, 82
4, 12, 36, 108
4, 14, 38, 110
3 points
Question 11
Find the indicated sum.
Answer
46
60
14
24
3 points
Question 12
Find the indicated sum.
Answer
3 points
Question 13
Find the indicated sum.
Answer
39
30
84
120
3 points
Question 14
Find the indicated sum.
Answer
45
110
74
120
3 points
Question 15
Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d.
Find a8 when a1 = -10, d = -3.
Answer
-31
11
-34
14
3 points
Question 16
Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d.
Find a21 when a1 = 28, d = -5.
Answer
-77
128
-100
-72
3 points
Question 17
Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20, the 20th term of the sequence.
1, 4, 7, 10, 13, . . .
Answer
an = 3n + 2; a20 = 62
an = n + 3; a20 = 23
an = 3n - 2; a20 = 58
an = 2n - 3; a20 = 37
3 points
Question 18
Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20, the 20th term of the sequence.
25, 16 , 7, -2, . . .
Answer
an = -9n + 25; a20 = -155
an = -9n + 34; a20 = -146
an = 9n - 25; a20 = 155
an = 9n - 34; a20 = 146
3 points
Question 19
Solve the problem.
The population of a town is increasing by 200 inhabitants each year. If its population at the beginning of 1990 was 27,842, what was its population at the beginning of 1998?
Answer
222,680 inhabitants
29,442 inhabitants
29,242 inhabitants
445,360 inhabitants
3 points
Question 20
Find the indicated sum.
Find the sum of the first 50 terms of the arithmetic sequence: 3, -4, -11, -18, . . .
Answer
-8600
-8425
-347
-8420
3 points
Question 21
Find the indicated sum.
Find the sum of the first 48 terms of the arithmetic sequence: 2, 4, 6, 8, . . .
Answer
98
2359
2400
2352
3 points
Question 22
Write out the first three terms and the last term of the arithmetic sequence.
Answer
-5 - 1 + 7 - . . . + 85
1 + 31 + 103 + . . . + 535
-5 + 1 + 7 + . . . + 85
1 + 7 + 13 + . . . + 85
3 points
Question 23
Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
Answer
-1522.5
-1421
-1595
-1537
3 points
Question 24
Solve the problem.
A theater has 32 rows with 20 seats in the first row, 25 in the second row, 30 in the third row, and so forth. How many seats are in the theater?
Answer
6400 seats
6240 seats
3120 seats
3200 seats
3 points
Question 25
If the given sequence is a geometric sequence, find the common ratio.
4, 16, 64, 256, 1024
Answer
4
16
not a geometric sequence
3 points
Question 26
If the given sequence is a geometric sequence, find the common ratio.
, , , ,
Answer
20
4
3 points
Question 27
Write the first five terms of the geometric sequence.
a1 = 7; r =
Answer
, , , ,
7, , , ,
7, , , , 8
7, 28, 112, 448, 1792
3 points
Question 28
Write the first five terms of the geometric sequence.
an = 5an-1; a1 = 3
Answer
15, 75, 375, 1875, 9375
3, 8, 13, 18, 23
5, 15, 75, 375, 1875
3, 15, 75, 375, 1875
3 points
Question 29
Use the formula for the sum of the first n terms of a geometric sequence to solve.
Find the sum of the first six terms of the geometric sequence: 3, 15, 75, . . . .
Answer
11718
93
3906
910
3 points
Question 30
Use the formula for the sum of the first n terms of a geometric sequence to solve.
Find the sum of the first 11 terms of the geometric sequence: -3, -6, -12, -24, -48, . . . .
Answer
-6161
-6139
-6141
-6104
3 points
Question 31
Use the formula for the sum of the first n terms of a geometric sequence to solve.
Find the sum of the first five terms of the geometric sequence: , , , . . . .
Answer
3 points
Question 32
Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.
Answer
-2460
-156
244
-7710
3 points
Question 33
Solve the problem.
A job pays a salary of 29,000 the first year. During the next 6 years, the salary increases by 6% each year. What is the salary for the 7th year? What is the total salary over the 7-year period? (Round to the nearest cent.)
Answer
$43,605.28; $287,026.57
$41,137.05; $243,421.29
$41,137.05; $202,284.24
$43,605.28; $202,300.9
Sure! I can help you with your midterm review. Here are the first four terms of each sequence:
1. Sequence: an = 3n - 1
First four terms: 2, 5, 8, 11
2. Sequence: an = 2(2n - 3)
First four terms: -6, -2, 2, 6
3. Sequence: an = 4n
First four terms: 4, 8, 12, 16
4. Sequence: an = (2/3)n
First four terms: 1, 2/3, 4/9, 8/27
5. Sequence: an = (-1)n(n + 5)
First four terms: -6, -14, -24, -36
6. Sequence: an = (-1)n + 1(n + 6)
First four terms: -7, 8, -9, 10
7. Sequence: an = ?
The sequence is incomplete and cannot be determined without additional information.
8. Sequence: a1 = -5 and an = an-1 - 3 for n ≥ 2
First four terms: -5, -2, 1, 4
9. Sequence: a1 = -6 and an = -2an-1 for n ≥ 2
First four terms: -6, 12, -24, 48
10. Sequence: a1 = 4 and an = 3an-1 + 2 for n ≥ 2
First four terms: 4, 14, 44, 134
I hope this helps with your midterm review! Let me know if you need any further assistance.
To find the first four terms of a sequence with the given general term, you simply substitute the values 1, 2, 3, and 4 into the general term equation and evaluate.
Let's go through each question step by step.
Question 1:
The general term is given as an = 3n - 1.
To find the first four terms, substitute n=1, n=2, n=3, n=4 into the equation:
a1 = 3(1) - 1 = 2
a2 = 3(2) - 1 = 5
a3 = 3(3) - 1 = 8
a4 = 3(4) - 1 = 11
Therefore, the first four terms are 2, 5, 8, 11.
Question 2:
The general term is given as an = 2(2n - 3).
To find the first four terms, substitute n=1, n=2, n=3, n=4 into the equation:
a1 = 2(2(1) - 3) = -2
a2 = 2(2(2) - 3) = 2
a3 = 2(2(3) - 3) = 6
a4 = 2(2(4) - 3) = 10
Therefore, the first four terms are -2, 2, 6, 10.
Continue this process for each of the questions, substituting the values of n and evaluating the general term equation to find the first four terms of each sequence.