So I dont understand explicit equations Whats the formula an

So I don\'t understand explicit equations. Whats the formula and how are they different than recursive?

Solution

in explicit formula we just need to know the term number to find any term of the sequence

whereas in recursive formula each term is defined by its preceding term.so to find any term of the sequence we must know the preceding term

lets understand by an example

let a sequence be 1, 4 , 7 , 10 ...

a1 = 1 , difference between 2 terms = 3

for explicit formula

an = a1 + (n-1)*3

we just need to plug the value of n to get any term of the sequence

for recursive formula

an+1 = an + 3

to get any term of the sequence we need to know the preceding term

for eaxample

to find a3 we plug n = 2

a2+1 = a2 + 3

a3 = a2+ 3

tehrefore we need to know a2 term to get a3 term