Write a rule for the nth term of the arithmetic sequence. d = 2, a_1 = 5 d = -3,

Question

Write a rule for the nth term of the arithmetic sequence. d = 2, a_1 = 5 d = -3, a_2 = 18 d = 1/2, a_5 = 20 a_8 = 12, a_15 = 61 a_5 = 10, a_12 = 24 a_10 = 8, a_16 = 32 Find the sum of the first 10 terms of the arithmetic series. 2 + 6 + 10 + 14 + 18 + ... 3 + 7/2 + 4 + 9/2 + 5 + ... 6 + 3 + 0 + (-3) + (-6) + ... 0.7 + 1.9 + 3.1 + 4.3 + 5.5 + ... Suppose a movie theater has 42 rows of seats and there are 29 seats in the first row. Each row after the first has two more seats than the row before it. How many seats are in the theater?

Explanation / Answer

an = a1+(n-1)d

4) an = 5 + (n-1)2 = 2n+3

5) a2 = a1 +d

a1= a2-d = 18+3 = 21

Thus, an = 21 + (n-1)(-3) = 24-3n

6)a5=a1+4d

a1 = 20-4(1/2) = 18

an = 18 + (n-1)(1/2)

7) a15-a8 = (15-8)d

d= 7,

a8 = a1 +7d

a1 = 12 - 7(7) =12-49=-37.

Thus, an = -37 + (n-1)7 = 7n-44.

8) a12 - a5 = (12-5)d =7d

14=7d

d=2

a5=10=a1+4(2)

a1=2

Thus, an= 2+(n-1)2 = 2n

9)a16 - a10 = 6d

24=6d

d=4.

a10 = a1+9d

a1= 8-9(4) = 8-36=-28.

Thus, an=-28 +(n-1)(4) = 4n-32

For questions 10,11,12 and 13

Sum of Arithmetic series with n terms is, S= (n/2)[2a1+(n-1)d]

Thus for 10 terms, n=10

Thus, S= 5[2a1+9d] = 10a1+45d

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