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:

recursive form for AS. Explicit form for AS. 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.