# Which is an arithmetic sequence ?

## Answers

Step-by-step explanation:

I don’t know what you mean by which because there is no image but an arithmetic sequence is An Arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2.

I have the first 8 answers for you:

1: 1126

2: -370

3:

4:

5: 192

6: 870

7: 5414

8: 1308

The formula for #1 would be . Using 60 for n, we have

418+12(60-1) = 1126

The formula for #2 would be . Using 23 for n, we have

-18-16(23-1) = -370

The general form for this sequence is , where a₁ is the first term and d is the common difference. For #3, the first term is 45 and the common difference is -15. For #4, the first term is -87 and the common difference is 14.

For #5-8, add together the terms.

Step-by-step explanation:

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.

I have the first 8 answers for you:

1: 1126

2: -370

3: [tex]a_n=45-15(n-1)[/tex]

4: [tex]a_n=-87+14(n-1)[/tex]

5: 192

6: 870

7: 5414

8: 1308

The formula for #1 would be [tex]a_n=418+12(n-1)[/tex]. Using 60 for n, we have

418+12(60-1) = 1126

The formula for #2 would be [tex]a_n=-18-16(n-1)[/tex]. Using 23 for n, we have

-18-16(23-1) = -370

The general form for this sequence is [tex]a_n=a_1+d(n-1)[/tex], where a₁ is the first term and d is the common difference. For #3, the first term is 45 and the common difference is -15. For #4, the first term is -87 and the common difference is 14.

For #5-8, add together the terms.

i dont know sorry

step-by-step explanation:

Hello!

volume of sphere =4/3.pi.r^3