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Write all the key points of Arithmetic progression.



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Answer 1

Answer:

Arithmetic Progression (AP) is a sequence of numbers in order in which the difference of any two consecutive numbers is a constant value. For example, the series of natural numbers: 1, 2, 3, 4, 5, 6,… is an AP, which has a common difference between two successive terms (say 1 and 2) equal to 1 (2 -1).

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Answer 2

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★ Arithmetic Progression

Definition: An arithmetic progression is a sequence of the form: a,a+d, a +2d...a+nd... where the initial term a and the common difference d are real numbers. Examples:

1. Let a = -1 and d = 4:

{n} = (80, 81, 82, 83, 84.) = (-1,3,7, 11, 15,...}

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FORMULAS OF AP:

1. Let a be the first term and d be the common difference of the AP. now, n term of the AP is given by

• $\large \underline{\boxed{\bold{\pink{\sf \: a_n = a + (n-1)d}}}}$

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2. Let a be the first term and d be the common difference. Now, sum of first n terms of the AP is given by :

• $\large \underline{\boxed{\bold{\pink{\sf \: S_n= \frac{1}{2}[2 a+ (n-1)d]}}}}$

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3. Let a be the first term and a, be the last term of the AP. now. S_n = (a + a_n)

• $\large \underline{\boxed{\bold{\pink{\sf \: S_n= \frac{n}{2} [ (a+a_n) ]}}}}$

4. Let S, be the sum of first n terms of AP. then sum of first (n-1) terms of the AP is S₁.

• $\large \underline{\boxed{\bold{\pink{\sf \:a_n=S_n-S_{a-1}}}}}$

5. If the number of terms in the AP is odd, then there will be only one middle^th term.

• $\red{\sf \: middle \: term =( \frac{n + 1}{2} ) term}$

If the number of terms in the AP is even, then there will be 2 middle terms.

• $\red{ \sf \: first \: middle \: term = ( \frac{n}{2} )^{th} term}$
• $\red{ \sf \: second \: middle \: term = ( \frac{n + 1}{2} )^{th} term}$

6. Let I be the last term and d be the common difference of AP.

Now, nth term from the end=

• $\large \underline{\boxed{\bold{\pink{\sf \:[l-(n-1)d] }}}}$

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