Home
Class 12
MATHS
If the sum of n , 2n , 3n terms of an AP...

If the sum of `n , 2n , 3n` terms of an AP are `S_1,S_2,S_3` respectively . Prove that `S_3=3(S_2-S_1)`

Text Solution

AI Generated Solution

To prove that \( S_3 = 3(S_2 - S_1) \) where \( S_1, S_2, \) and \( S_3 \) are the sums of \( n, 2n, \) and \( 3n \) terms of an arithmetic progression (AP), we will follow these steps: ### Step 1: Write the formula for the sum of the first \( n \) terms of an AP The sum of the first \( n \) terms of an AP is given by the formula: \[ S_n = \frac{n}{2} \left(2a + (n - 1)d\right) \] where \( a \) is the first term and \( d \) is the common difference. ...
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERICISE 5.4|13 Videos

  • PROGRESSION AND SERIES

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERICISE 5.5|10 Videos

  • PROGRESSION AND SERIES

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERICISE 5.2|10 Videos

  • PROBABILITY II

    CENGAGE ENGLISH|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Archives (Numerical Value Type)|3 Videos

Similar Questions

Explore conceptually related problems

The sum of n, 2n, 3n terms of an A.P. are S_1, S_2, S_3 respectively. Prove that S_3 = 3(S_2 - S_1)

The sum of n ,2n ,3n terms of an A.P. are S_1S_2, S_3, respectively. Prove that S_3=3(S_2-S_1)dot

If the sum of n, 2n, 3n terms of an A.P are S_(1), S_(2), S_(3) , respectively, prove that S_(3) = 3 (S_(2) -S_(1)).

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

Let the sum of n, 2n, 3n terms of an A.P. be S_(1), S_(2) and S_(3) respectively. Show that S_(3) = 3(S_(2) - S_(1)) .

If the sum of n, 2n and infinite terms of G.P. are S_(1),S_(2) and S respectively, then prove that S_(1)(S_(1)-S)=S(S_(1)-S_(2)).

The sums of n terms of three arithmetical progressions are S_1, S_2 and S_3dot The first term of each unity and the common differences are 1,2 and 3 respectively. Prove that S_1+S_3=2S_2dot

The sums of n terms of three arithmetical progressions are S_1, S_2 and S_3dot The first term of each unity and the common differences are 1,2 and 3 respectively. Prove that S_1+S_3=2S_2dot

If S_1,S_2a n dS_3 be respectively the sum of n, 2n and 3n terms of a G.P., prove that S_1(S_3-S_2)=(S_2-S_1)^2

The sums of n terms of three arithmetical progressions are S_1, S_2 and S_3dot The first term of each unityand the common differences are 1,2 and 3 respectively. Prove that S_1+S_3=2S_2dot