SOLUTION: direction: write a rule for the nth term of the arithmetic sequence 30. d=4, a14=46 31. d=-12, a1=80. the answer is an = 92-12n but how? 32. d=5/3, a8=24 33. a5=17, a15=77 3

Algebra ->  Exponents -> SOLUTION: direction: write a rule for the nth term of the arithmetic sequence 30. d=4, a14=46 31. d=-12, a1=80. the answer is an = 92-12n but how? 32. d=5/3, a8=24 33. a5=17, a15=77 3      Log On


   

Question 550735: direction: write a rule for the nth term of the arithmetic sequence
30. d=4, a14=46
31. d=-12, a1=80. the answer is an = 92-12n but how?
32. d=5/3, a8=24
33. a5=17, a15=77
34. d=-6, a12=-4
35. a2=-28, a20=52
37. a7=34, a18=122
please show me the work with each of these problems so i could understand the concept behind it a little bit better. thanks for ur help and happy new year!
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for all of them is an = a1 + (n-1)d

direction: write a rule for the nth term of the arithmetic sequence

30. d=4, a14=46

an = a1 + (n-1)d
a14 = a1 + (14-1)(4)
46 = a1 + 13(4)
46 = a1 + 52
-6 = a1

an = a1 + (n-1)d
an = -6 + (n-1)(4)
an = -6 + 4n - 4
an = 4n - 10

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31. d=-12, a1=80. 

an = a1 + (n-1)d
an = 80 + (n-1)(-12)
an = 80 - 12n + 12
an = 92 - 12n

--------------------------

32. d=5/3, a8=24

an = a1 + (n-1)d
a8 = a1 + (8-1)(5%2F3)
24 = a1 + (7)(5%2F3)
24 = a1 + 35%2F3
3·24 = 3a1 + 35
72 = 3a1 + 35
37 = 3a1
37%2F3 = a1

an = a1 + (n-1)d
an = 37%2F3 + (n-1)(5%2F3)

3an = 37 + (n-1)5
3an = 37 + 5n - 5
3an = 32 + 5n
 an = %2832%2B5n%29%2F3

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33. a5=17, a15=77

an = a1 + (n-1)d
a5 = a1 + (5-1)d
17 = a1 + 4d

an = a1 + (n-1)d
a15 = a1 + (15-1)d
77 = a1 + 14d

Solve system of equations:

system%28a1%2B4d=17%2Ca1%2B14d=77%29

get a1 = -7, d = 6

an = a1 + (n-1)d
an = -7 + (n-1)(6)
an = -7 + 6n - 6
an = 6n - 13

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34. d=-6, a12=-4

an = a1 + (n-1)d
a12 = a1 + (12-1)(-6)
-4 = a1 + (11)(-6)
-4 = a1 - 66
62 = a1

an = a1 + (n-1)d
an = 62 + (n-1)(-6)
an = 62 - 6(n-1)
an = 62 - 6n + 6
an = 68 - 6n

You do the last two.  They're like 33.

35. a2=-28, a20=52
37. a7=34, a18=122

Edwin