SOLUTION: given the sequence: 5,8,11,......,101 find the number of terms

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Question 761754: given the sequence: 5,8,11,......,101 find the number of terms
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
given the sequence: 5,8,11,......,101 find the number of terms

a1 = first term = 5

d = a2 - a1 = 8 - 5 = 3
d = a3 - a2 = 11 - 8 = 3

Since those are the same, the sequence is arithmetic.

an = a1 + (n-1)d
101 = 5 + (n - 1)(3)
101 = 5 + 3(n - 1)
101 = 5 + 3n - 3
101 = 2 + 3n
 99 = 3n
 33 = n

Checking:
 
  5,8,11,14,17,20,23,26,29,32,35,
38,41,44,47,50,53,56,59,62,65,68,
71,74,77,80,83,86,89,92,95,98,101

Count them.  There are 33 of them.

Edwin
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