Write a recursive formula and an explicit formula for the following arithmetic sequence

Question

9,11,13,15,17

Answer 1

9,11,13,15,17,...

is an arithmetic sequence with common difference =2 = d,

and first term = 9 = a1

nth term = an = a1+d(n-1)

for a recursive formula

an = an-1 + d

an = an-1 = 2

each term is 2 more than the previous term

for an, an-1 is the previous term

to avoid confusing an-1 with (an)-1

maybe it's better to write the previous term as a(n-1)

maybe. as that also looks confusingly similar to multiplication of two terms

subscripts might be the best way to go

a_n = a_n-1 +2

a_n = a₁ +d(n-1)

a₅ = 9 +2(5-1) = 9+2(4) = 9+6 = 17

or

a₅ = a₄ + 2 = 15+2 = 17