Writing an explicit equation

Question

Write an explicit sequence for 4,9,14,19,24 and what is it’s 99th term

2) what is t(4)=12 t(10)=48 explicit equation and it’s 18th term

Answer 1

f(t)=a₁+d(n-1) where a₁=first term, d=common difference, n=the number of the term

f(t)=4+(5)(n-1)

f(99)=4+(5)(99-1)

f(99)=4+(5)(98)

f(99)=4+490

f(99)=494

t(4)=12 and t(10)=48

we have to add some number 6 times because we are missing...

t(5), t(6), t(7), t(8), t(9), and we have to add this number to t(9) to get t(10)

12+6d=48

6d=36

d=6, the common difference

now go backwards to get t(1), the first term

12-6=6, 6-6=0, 0-6=-6

-6 is the first term

-6, 0, 6, 12, 18, 24, 30, 36, 42, 48, ... is the sequence

t(x)=-6+6(n-1) is the formula

t(18)=-6+6(18-1)

t(18)=-6+6(17)

t(18)=-6+102

t(18)=96