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
