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

Write the formula of the sum of first n terms for an A.P.

Advertisements
Advertisements

प्रश्न

Write the formula of the sum of first n terms for an A.P.

बेरीज
Advertisements

उत्तर

Sum of the first n terms is given by

`S_n = n/2[2a + (n - 1)d]`,

where a = first term,

d = common difference

OR

`S_n = n/2(t_1 + t_n)`,

where t1 = first term,

tn = last term

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Arithmetic Progression - Q.1 (B)

संबंधित प्रश्‍न

Find the sum of the following arithmetic progressions:

1, 3, 5, 7, ... to 12 terms


Find the sum of first 22 terms of an A.P. in which d = 22 and a = 149.


In an A.P., if the 5th and 12th terms are 30 and 65 respectively, what is the sum of first 20 terms?


How many three-digit numbers are divisible by 9?


Find an AP whose 4th  term is 9 and the sum of its 6th and 13th terms is 40. 


Find the sum of all even numbers between 1 and 350.

Sum of 1 to n natural numbers is 36, then find the value of n.


There are 37 terms in an A.P., the sum of three terms placed exactly at the middle is 225 and the sum of last three terms is 429. Write the A.P.


Find the sum:  1 + 3 + 5 + 7 + ... + 199 .


The sum of first 9 terms of an A.P. is 162. The ratio of its 6th term to its 13th term is 1 : 2. Find the first and 15th term of the A.P.


The sum of first n terms of an A.P. is 3n2 + 4n. Find the 25th term of this A.P.

 

A piece of equipment cost a certain factory Rs 60,000. If it depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?


If 18th and 11th term of an A.P. are in the ratio 3 : 2, then its 21st and 5th terms are in the ratio


The common difference of the A.P.

\[\frac{1}{3}, \frac{1 - 3b}{3}, \frac{1 - 6b}{3}, . . .\] is 
 

The first three terms of an A.P. respectively are 3y − 1, 3y + 5 and 5y + 1. Then, y equals


Find the sum of first 1000 positive integers.

Activity :- Let 1 + 2 + 3 + ........ + 1000

Using formula for the sum of first n terms of an A.P.,

Sn = `square`

S1000 = `square/2 (1 + 1000)`

= 500 × 1001

= `square`

Therefore, Sum of the first 1000 positive integer is `square`


Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.

[Hint (iii) : These numbers will be : multiples of 2 + multiples of 5 – multiples of 2 as well as of 5]


Find the sum of the integers between 100 and 200 that are

  1. divisible by 9
  2. not divisible by 9

[Hint (ii) : These numbers will be : Total numbers – Total numbers divisible by 9]


Find the sum of first seven numbers which are multiples of 2 as well as of 9.


If 7 times the seventh term of the AP is equal to 5 times the fifth term, then find the value of its 12th term.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×