Question

Constructing arithmetic sequences Learn Recursive formulas for arithmetic sequences(Opens a modal)Recursive formulas for arithmetic sequences(Opens a modal)Explicit formulas for arithmetic sequences(Opens a modal)Explicit formulas for arithmetic sequences(Opens a modal)Arithmetic sequence problem(Opens a modal)Converting recursive

Answer 1

Answer:

Step-by-step explanation:

To Find :

1. recursive form for AS.
2. Explicit form  for AS.
3. Arithmetic  Sequence problem.    

Solution:

Recursive form :

Not all certain can defined in terms of recursive format .

In this form each term depends upon the preceding term .

It is formulated by starting term a and depends upon before term An-1.

It is like ladder structure

a2=a1+"step up".

Recursive formula as ,

F(n)=F(n-1)+d. ......... d is refered as the step up in the  arithmetic sequence.

E.g.   10,  15,  20, 25..

step up is 5 units

hence for third term is ,

a3=a2+5=15+5=20.

hence proved by formula in recursive form.

Explicit Form:

This form will creates a sequence using n, and number term at that location.

i.e. It is formulated as the 1st and (one less than term number * common difference ).

F(n)=F(1)+d(n-1).

for same  above example

f(3)=10+5(3-1)=10+5(2)=10+10=20.

hence proved same result using two different  formula .

Arithmetic sequence problem:

consider as sequence :

-6, -1, 4, ?.

here common difference as

-1-(-6)=5     ,4-(-1)=5.

hence d=5.

F(4)=F(1)+d(4-1).

     =  -6+5(3)=  -6  +15 =9.

The next term is 9 using explicit formula

now by recursive form

a4=a3+5=4+5=9

The 4th term is 9.

Hence in both forms term being same as "9".

Depending upon the sequence chose proper method to solve sequences.