On the space provided, write A if the sequence is Arithmetic and NA if not an Arithmetic. 1. 2, 4, 6, 8, ... 2. 3, 6, 10, 15, ... 3. -3, -1, 1, 3, ... 4. 5, 10, 20, 40, ... 5. 1, 5, 9, 13, 17, ... Answer by solving the following numbers (in a separate sheet) for 5 pts each 1. What are the three arithmetic means between 4 and 16? 2. Find the sum of the first 16 terms of the arithmetic sequence 9, 12, 15, 18,... 3. Find the 10th term of the arithmetic sequence -6, -2,2, 6, 10,...
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Verified answer
Step-by-step explanation:
A.
B.[tex]a_{n} =a_{1} + (n - 1)d [/tex]
1.
[tex]16 = 4 + (5 - 1)d \\ 16 = 4 + 4d \\ 16 - 4 = 4 - 4 + 4d \\ 16 - 4 = 4d \\ 12 = 4d[/tex]
[tex] \frac{12}{4} = \frac{4d}{4} \\ 3 = d [/tex]
[tex]a_{2} =4 + (2 - 1)3 \\ = 4 + 1(3) \\ = 4 + 3 = 7[/tex]
[tex]a_{3} =4 + (3 - 1)3 \\ = 4 + 2(3) \\ 4 + 6 = 10[/tex]
[tex]a_{4} =4 + (4 - 1)3 \\ = 4 + 3(3) \\ 4 + 9 = 13[/tex]
2.
[tex]s_{n} = \frac{n}{2} (2a_{1} + (n - 1)d)[/tex]
[tex]s_{n} = \frac{16}{2} (18 + (16 - 1)3) \\ = \frac{16}{2} (18+ 15(3))[/tex]
[tex]= \frac{16}{2} (18 + 45) \\ = \frac{16}{2} (63) = 8(63) \\ s_{16} = 504[/tex]
3.
[tex]a_{10} = - 6 + (10 - 1) 8 \\ = - 6 + 9(8) \\ = - 6 + 72 \\ a_{10} = 66[/tex]