Terms of sequence

Question

How many terms does the following sequence have? 

15,15+3,15+6,15+9,...,15+39

Answer 1

15+0, 15+3, 15+6, 15+9,...15+39

 

each term is 15 + a multiple of 3 starting with the first multiple of 3 which is 0

39/3=13+1=14 terms  (the 1 comes from the first multiple of 3 which again is 0)

 

Answer 2

 

 

This is arithmetic sequence

 

15,15+3,15+6,15+9,...,15+39

 

Formula for arithmetic sequence is

 

An=a1+(n-1)d

 

 a1=15

d=+3

An=15+39=54

n=?

 

An=15+(n-1)3

54=15+3n-3

54=3n+12

42=3n

14=n

 

There are 14 terms

 

Answer 3

Each term is 3 more than the previous term and can be represented as s_n:

 

s_n = 15 + 3*(n - 1) = 12 + 3n

 

Then the last term is 12 + 3n = 15 + 39 = 54

3n = 54 - 12 = 42

n = 14

 

There are 14 terms in this sequence.