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महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता १० वी

Select the Correct Alternative and Write It. What is the Sum of First N Natural Numbers ?

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प्रश्न

Select the correct alternative and write it. 

What is the sum of first n natural numbers ? 

 

पर्याय

  • (A)` (n(n-1))/2` 

  • (B)`n/2(n-2)`

  • (c)` n(n+1)/2` 

  • (D) `(n(n+2))/2`

MCQ
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उत्तर

(c) `(n(n+1))/2`

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2018-2019 (March) Balbharati Model Question Paper Set 3

संबंधित प्रश्‍न

Find the sum of  the following arithmetic series:

`7 + 10 1/2 + 14 + ... + 84`


Decide whether the following sequence is an A.P., if so find the 20th term of the progression:

–12, –5, 2, 9, 16, 23, 30, ..............


Given Arithmetic Progression 12, 16, 20, 24, . . . Find the 24th term of this progression.


Find the 19th term of the following A.P.:

7, 13, 19, 25, ...


Find the 27th term of the following A.P.
9, 4, –1, –6, –11,...


If the sum of first n terms of an AP is n2, then find its 10th term.


How many multiples of 4 lie between 10 and 205?


If third term and fifth term of an A.P. are 13 and 25 respectively, find its 7th term.


Find tn if a = 20 and d = 3.


Decide whether the given sequence 24, 17, 10, 3,...... is an A.P.? If yes find its common term (tn).


How many two-digit numbers are divisible by 5?

Activity :-  Two-digit numbers divisible by 5 are, 10, 15, 20, ......, 95.

Here, d = 5, therefore this sequence is an A.P.

Here, a = 10, d = 5, tn = 95, n = ?

tn = a + (n – 1) `square`

`square` = 10 + (n – 1) × 5

`square` = (n – 1) × 5

`square` = (n – 1)

Therefore n = `square`

There are `square` two-digit numbers divisible by 5.


Decide whether 301 is term of given sequence 5, 11, 17, 23,.....

Activity :-  Here, d = `square`, therefore this sequence is an A.P.

a = 5, d = `square`

Let nth term of this A.P. be 301.

tn = a + (n – 1) `square`

301 = 5 + (n – 1) × `square`

301 = 6n – 1

n = `302/6` = `square`

But n is not positive integer.

Therefore, 301 is `square` the term of sequence 5, 11, 17, 23,......


12, 16, 20, 24,...... Find 25th term of this A.P.


If p - 1, p + 3, 3p - 1 are in AP, then p is equal to ______.


Find a and b so that the numbers a, 7, b, 23 are in A.P.


In an A.P. if the sum of third and seventh term is zero. Find its 5th term.


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