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Solution - Arithmetic sequences

The common difference equals: 200
-200
The sum of the sequence equals: 1204
-1204
The explicit formula of this sequence is: an=1+(n1)(200)
a_n=-1+(n-1)*(-200)
The recursive formula of this sequence is: an=a(n1)200
a_n=a_((n-1))-200
The nth terms: 1,201,401,601,801,1001,1201...
-1,-201,-401,-601,-801,-1001,-1201...

Other Ways to Solve

Arithmetic sequences

Step-by-step explanation

1. Find the common difference

Find the common difference by subtracting any term in the sequence from the term that comes after it.

a2a1=2011=200

a3a2=401201=200

a4a3=601401=200

The difference of the sequence is constant and equals the difference between two consecutive terms.
d=200

2. Find the sum

Calculate the sum of the sequence using the sum formula:

Sum=(n(a1+an))/2

Sum=(n*(a1+an))/2

Plug in the terms.

Sum=(4*(a1+an))/2

Sum=(4*(-1+an))/2

Sum=(4*(-1+-601))/2

Simplify the expression.

Sum=(4*(-1+-601))/2

Sum=(4*-602)/2

Sum=24082

Sum=1204

The sum of this sequence is -1204.

This series corresponds to the following straight line y=200x+1

3. Find the explicit form

The formula for expressing arithmetic sequences in their explicit form is:
an=a1+(n1)d

Plug in the terms.
a1=1 (this is the 1st term)
d=200 (this is the common difference)
an (this is the nth term)
n (this is the term position)

The explicit form of this arithmetic sequence is:

an=1+(n1)(200)

4. Find the recursive form

The formula for expressing arithmetic sequences in their recursive form is:
an=a(1n)+d

Plug in the d term.
d=200 (this is the common difference)

The recursive form of this arithmetic sequence is:

an=a(n1)200

5. Find the nth element

a1=a1+(n1)d=1+(11)200=1

a2=a1+(n1)d=1+(21)200=201

a3=a1+(n1)d=1+(31)200=401

a4=a1+(n1)d=1+(41)200=601

a5=a1+(n1)d=1+(51)200=801

a6=a1+(n1)d=1+(61)200=1001

a7=a1+(n1)d=1+(71)200=1201

Why learn this

When will the next bus arrive? How many people can fit inside a stadium? How much money will I earn this year? All these questions can be answered by learning how arithmetic sequences work. The progression of time, triangular patterns (bowling pins, for example), and increases or decreases in quantity can all be expressed as arithmetic sequences.

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