Question

Write a recursive rule and an explicit rule for the arithmetic sequence

Answer 1

a1 = 35
a2 = 32 = 35 - 3 = a1 - 3
Recursive formular:
`a_(n+1)=a_n-3`
a = 35, d = -3
Tn = a + (n - 1)d = 35 + (n - 1)-3 = 35 - 3n + 3 = 38 - 3n
Explicit formular is Tn = 38 - 3n

a1 = 65
a2 = 72 = 7 + 65 = 7 + a1
Recursive formula is
`a_(n+1)=7+a_n`
a = 65, d = 7
Tn = a + (n - 1)d = 65 + (n - 1)7 = 65 + 7n - 7 = 58 + 7n
Explicit formula is 58 + 7n