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

Step-by-step explanation:

To Find :

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.

correct answer is infinitely many solutions

step-by-step explanation:

2(2x + 3) = -4 + 2(2x + 5)

solving the above equation:

4x + 6 = -4 +4x +10

combining like terms

4x -4x = -4+10-6

0=0

since both sides are 0=0, we end up into true statement it means it has infinite many solutions.

so correct answer is infinitely many solutions