SOLUTION: Write a rule for the nth turn of the arithmetic sequence. Then find a(20). 1,4,7,10,13

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Question 775076: Write a rule for the nth turn of the arithmetic sequence. Then find a(20).
1,4,7,10,13
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
1,4,7,10,13

To get the 2nd term 4, you add 3 to the 1st term 1 time
To get the 3rd term 7, you add 3 to the 1st term 2 times
To get the 4th term 10, you add 3 to the 1st term 3 times.
To get the 5th term 13, you add 3 to the 1st term 4 times.

To get the nth term an, you add 3 to the 1st term (n-1) times.

an = a1 + (n-1)·d

Substitute a1 = first term = 1 and d = 3 (the common
difference between any term and the one before it.

an = 1 + (n-1)·3 = 1 + 3(n-1) = 1 + 3n - 3 = 3n-2.

an = 3n-2

Substitute n=20:

a20 = 3(20)-2 = 60-2 = 58. 

Checking:
1,4,7,10,13,16,19,22,25,28,31,34,37,40,43,46,49,52,55,58

Edwin
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