Arithmetic sequence

Question

Is this sequence arithmetic? 51,47,43,39, . . If. so, write a recursive and an explicit formula to represent it. Then find the 3th, 5th and 15th terms of the sequence above.

Answer 1

a_n=a₁+(n-1)d

a_n=51+(n-1)(-4)

a_n=51-4n+4

a_n=55-4n is the explicit formula

a_n=a_n-1+(-4) is the recursive formula

the third term is 43

the fifth term is a₅=55-4(5)=55-20=35

the fifteenth term is a₁₅=55-4(15)=55-60=-5