Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Let the sum of n, 2 n, 3 n terms of an A.P. be S 1, S 2 and S 3, respectively, show that S 3 = 3 (S 2 minus S 1)

3.  Let the sum of n, 2n, 3n terms of an A.P. be S_1 , S_2 , S_3, respectively, show that S_3 = 3(S_2 - S_1)

Answers (1)

best_answer

Let a be first term and d be common difference of AP.

S_n=\frac{n}{2}[2a+(n-1)d]=S_1..................................1

S_2n=\frac{2n}{2}[2a+(2n-1)d]=S_2..................................2

S_2_n=\frac{3n}{2}[2a+(3n-1)d]=S_3..................................3

Subtract equation 1 from 2,

S_2-S_1=\frac{2n}{2}[2a+(2n-1)d]-\frac{n}{2}[2a+(n-1)d]

                =\frac{n}{2}[4a+4nd-2d-2a-nd+d]

               =\frac{n}{2}[2a+3nd-d]

               =\frac{n}{2}[2a+(3n-1)d]

\therefore 3(S_2-S_1)=\frac{3n}{2}[2a+(3n-1)d]=S_3

Hence, the result is proved.

Posted by

seema garhwal

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 12 Maths paper 2025 'moderate but lengthy', questions from PYQ, NCERT
anam-khan

CBSE Board Exam 2025 Live: Class 12 mathematics paper 'moderate but lengthy'; memory-based questions
anam-khan

CBSE Class 12 Chemistry Exam Analysis 2025: Paper 'moderately difficult' but well balanced

Latest Question