मराठी

In an A.P., if Sn = 3n2 + 5n and ak = 164, find the value of k. - Mathematics

Advertisements
Advertisements

प्रश्न

In an A.P., if Sn = 3n2 + 5n and ak = 164, find the value of k.

बेरीज
Advertisements

उत्तर

∵ nth term of an AP,

an = Sn – Sn – 1

= 3n2 + 5n – 3(n – 1)2 – 5(n – 1)   ...[∵ Sn = 3n2 + 5n (Given)]

= 3n2 + 5n – 3n2 – 3 + 6n – 5n + 5

⇒ an = 6n + 2    ...(i)

or ak = 6k + 2 = 164   ...[∵ ak = 164 (Given)]

⇒ 6k = 164 – 2 = 162

∴ k = 27

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Arithematic Progressions - Exercise 5.3 [पृष्ठ ५४]

संबंधित प्रश्‍न

Find the 9th term from the end (towards the first term) of the A.P. 5, 9, 13, ...., 185


In an AP: Given a = 5, d = 3, an = 50, find n and Sn.


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


In an AP given d = 5, S9 = 75, find a and a9.


The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.


If the sum of the first n terms of an AP is 4n − n2, what is the first term (that is, S1)? What is the sum of the first two terms? What is the second term? Similarly, find the 3rd, the 10th, and the nth terms.


If a denotes the nth term of the AP 2, 7, 12, 17, … find the value of (a30 - a20 ).


In an A.P. 19th term is 52 and 38th term is 128, find sum of first 56 terms. 


Simplify `sqrt(50)`


The sum of first n terms of an A.P. is 5n − n2. Find the nth term of this A.P.

 

If `4/5` , a, 2 are three consecutive terms of an A.P., then find the value of a


Q.12


Q.16


Q.17 


If an = 3 – 4n, show that a1, a2, a3,... form an AP. Also find S20.


Shubhankar invested in a national savings certificate scheme. In the first year he invested ₹ 500, in the second year ₹ 700, in the third year ₹ 900 and so on. Find the total amount that he invested in 12 years


Find the sum:

`4 - 1/n + 4 - 2/n + 4 - 3/n + ...` upto n terms


Find the sum of the integers between 100 and 200 that are not divisible by 9.


The 5th term and the 9th term of an Arithmetic Progression are 4 and – 12 respectively.

Find:

  1. the first term
  2. common difference
  3. sum of 16 terms of the AP.

The sum of 40 terms of the A.P. 7 + 10 + 13 + 16 + .......... is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×