हिंदी

What is the Sum of First N Terms of the Ap A, 3a, 5a, ….. - Mathematics

Advertisements
Advertisements

प्रश्न

What is the sum of first n terms of the AP a, 3a, 5a, …..

Advertisements

उत्तर

The given AP is 3a,5a,........
Here,
First term, A = a
Common difference, D = 3a - a = 2a
 ∴ Sum of the n terms, n S

`= n/2 [2xx a+ (n-1) xx 2a]          { s_n = n/2 [ 2A +(n-1) D]}`

`= n/2 (2a + 2an -2a )`

`= n/2 xx 2 an`

= an2

Hence, the required sum is an2 .

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 11: Arithmetic Progression - Exercises 3

APPEARS IN

आर.एस. अग्रवाल Mathematics [English] Class 10
अध्याय 11 Arithmetic Progression
Exercises 3 | Q 9

संबंधित प्रश्न

 In an AP Given a12 = 37, d = 3, find a and S12.


A contract on a construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs. 200 for the first day, Rs. 250 for the second day, Rs. 300 for the third day, etc., the penalty for each succeeding day being Rs. 50 more than for the preceding day. How much money does the contractor have to pay as a penalty  if he has delayed the work by 30 days.


Find the sum of the following arithmetic progressions 

`(x - y)^2,(x^2 + y^2), (x + y)^2,.... to n term`


Find the sum 25 + 28 + 31 + ….. + 100


Find the sum of the first 15 terms of each of the following sequences having the nth term as

`a_n = 3 + 4n`


Is 184 a term of the AP 3, 7, 11, 15, ….?


If the pth term of an AP is q and its qth term is p then show that its (p + q)th term is zero


If 18, a, (b - 3) are in AP, then find the value of (2a – b)


How many terms of the AP 63, 60, 57, 54, ….. must be taken so that their sum is 693? Explain the double answer.


Find the sum of all multiples of 9 lying between 300 and 700.


Find the first term and common difference for  the A.P.

0.6, 0.9, 1.2,1.5,...


Choose the correct alternative answer for the following question.

For an given A.P. a = 3.5, d = 0, n = 101, then tn = ....


The sum of 5th and 9th terms of an A.P. is 30. If its 25th term is three times its 8th term, find the A.P.


Write the sum of first n even natural numbers.

 

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. is \[\frac{1}{2q}, \frac{1 - 2q}{2q}, \frac{1 - 4q}{2q}, . . .\] is 

 

Q.5 


If a = 6 and d = 10, then find S10 


If the numbers n - 2, 4n - 1 and 5n + 2 are in AP, then the value of n is ______.


Solve the equation:

– 4 + (–1) + 2 + 5 + ... + x = 437


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×